TL;DR I was bored today. Felt creative and went with it. It's all kind of long and vague.

In my opinion, Whoremaster is most entertaining as a "management" game. Depending on how much "RPG" that is planned, there are several more completed games (Overwhored, Harem Collector) available.
Interesting "Gameplay" system that could be translated into a "slumlord" setting would be RoTTK or Crusader Lord-ish with more "politicking" (to a degree) involved than forming a party and personally walking around for "events"
1)should player be able to name their character?
---I don't think it's critically important, but it's definitely nice and I think it's simple enough? Since you said you were going to add a family system, it'd add to that aspect
2) Should I allow People to Rename girls, yes even unique(as long as they are slaves, free girls No rename)
--Complete renames would be pointless. As others have said, tags/nicknames would be the best. Perhaps associate it with a "obedience" check so that it's perhaps a first lvl reward.
3) Should I allow Girls and random girls and (Spoiler!!!) Servants and Soldiers, And Captured Beasts) to have last names, or is a first name all we need?
---That should be under consideration depending on the type of girl
-------COMPLETE humanoid monsters (Sub-human level intellect) = A single name (similar to a pet).
-------Partial humanoids (Atleast human-level intellect) = premade names
-------Servants = based on their origin?
-----------------Orphans = wouldn't really have names. (I think the origins of this game would be the same right?) Incorporate with the "rename" system / an adoption event
-----------------Bought = would have names. Perhaps begin them as nameless generic "servant title" allow a reveal if they get into the "inner circle", but depends on how you want the servant system to operate.
-----------------Forced from your stable = Would have names. No generic "servant title"
(Maybe separating to this degree is excessive? To begin with though, a generic title into a "Rename"/reveal system would be more interesting)
4) Should i Give the player their choice of backgrounds?
It'd be definitely more interesting. I think the best way would be the set of traits/skills customization of "slave maker"?
But depends on how the rest of the gameplay spans out. This system should complement however the core gameplay works out to be.
5) Should i break sex images into seperate catagories(game will use folder per image tag not image name)
That would allow the game to be increasingly modable? (I think?) Increased organization is annoying at the start, but ultimately helps streamline future content
6) Would People like a custom mouse image?
No. I think this is cheesy and excessive. The cursor should retain original cursor shape. Maybe a simple recolor to suit the UI, but a new mouse image would be tacky.
7) how would people like to make the catacombs and part of the city to be more of a rpg, where you can walk around?
I think there are several ways to do this...
--Recettear system? An "Adventurer" girl is "coerced" into leading you through a dungeon?
------It could also be interesting with a type of "DnD" gameplay (Legend of Grimrock style)
(Though in my opinion more RPG aspects added, the more it'd dilute from the "brothel" gameplay.)

Would you all be opposed to Me making Whore Master Evolved a Partial rpg game?
--I don't think anyone would be opposed to you making the game as you envision it completely and I think everyone has different aspects of the game that they want more emphasized
In MY opinion, I think there are several games already with "Partial RPG" elements where the player goes out on adventures to "conquer" girls individually.
I think that level of gameplay is fine, but what has drawn ME to this game was the larger "management" type gameplay.
(Have you tried pytfall? Interesting game. Not sure how their development is going though: The girls are used in whore, but also you're a gladiator and you participate in "fights" with them. I think the overall theme was interesting, but it felt more like a gladiator RPG with a brothel system "tacked on". Perhaps "fingers in too many pies" syndrome?)
I'm not quite sure how much of the game you've already finished or if my ideas on the game are interesting, but here's an input for you to chew on.
---You're a slumlord (Original Whoremaster origin)
------Character Creation
-----------Origin
------------------Birth (Noble / Merchant / Orphan) (More options in the future perhaps)
------------------Traits (Cast Out / Born Evil / Supernatural Origins / Affinity for alchemy / etc etc)
--------First screen
-------------Perhaps with the "RPG" element you want added
-------------------Escaping from the guards/thugs/abusive father
-------------------Earning gold / Slaver licence / First girl
-------------------Combat (Killing abusive father / Killing a kind family that took you in for the night / Killing a small time boss)
---------Main Gameplay
---------------The familiar Whoremaster UI
---------------------Reducing the "Job types" to one
> (I always thought it didn't make any sense for the "Building types" to be mixable in the original)
----------------------Gang Management
>Perhaps scrapping the old gang system with a "Leader" system where you're recruiting the boss of thugs to work for you.
----The Boss traits will be applicable to the rest of the gang
----Men will still be the overall "gang" health, but ultimately require the "Boss" to be eliminated for the gang to be destroyed
----Could be a possible use for the males (if you want them. Doesn't really matter if you don't want males at all)
----Could be expanded to a bigger "Strategy" genre / Politicking
----Rival capturing / Your gang leaders betraying you etc etc could be added
All of what I'm saying is possible would be "story-wise" because coding-wise I'm sure anything could be made to fit
----------------------Catacombs
>The old system is a bit "Basic". With the addition of an RPG element, this could be more fleshed out
>Hard restriction on quality of "monster girls"/items based on stats.
>Interactive "Coersion" gameplay
>Dungeon Maou (Brood Queen) Element
>More easily adjusted difficulty than current system
>Possible to ignore altogether if you want
>>>>I think though, rather than "catacombs", maybe it should be more of "Breaking down homes" event? Kind of weird that even in a "fantasy" setting, there would be a random catacombs in the middle of a city
>>>>Also because I'm just fleshing out random ideas that's popping up (I mean this is pretty fun to think up possible stuff) maybe allow multiple "Dungeons" (Local School / Rival Brothel / Nunnery / Homes / Suburbs / etc) so that girls CAN be "restricted" to areas if the mod creators wanted that option
>>>>Also perhaps take into account basic skills rqm for each dungeon and allow "auto resolve" solution by sending just the girls for those who want to skip the RPG element.
----------------------Morality
------Sort of a random nut to crack. This could be a gating system that allows more "brazen" acts of kidnapping at the cost of a "rubber band" A.I. (The city guards) coming down on you hard.
Here's an example I threw together:
>>>> Lv 5 (Paragon) Girls from your "charity" (Large number of girls to choose from / More girls coerced at a time = exponential risk with the law / Very easy to coerce "Naive" girls)
>>>> Lv 4 (Legitimate) Employees (Higher quality than interns / Require high wages (Until complete obedient or through other means) / More difficult to succeed/ Lower Lawsuit chance)
>>>> Lv 3 (Small Time) Interns (High chance of lawsuit fail event to reduce rep/requires lower rebelliousness to succeed than evil/Less provocation of the law/Higher obedience on success)
>>>> Lv 2 (Nice) Date Rape (A Charisma check or drug or coersion/High risk with the law/Only possible once per day)
>>>> Lv 1 (Neutral) Orphans (Terrible quality / Little risk with the law / No cost )
>>>> Lv 2 (Thug) Local Prostitutes (Terrible Looks but Med sex skills / Slight risk with the law / Separate event consequences and rewards)
>>>> Lv 3 (Small Time) Escorts (Good Looks and sex skills / Med risk with the law / Separate event consequences and rewards)
>>>> Lv 4 (Boss) Kidnapping (Good Looks and Good traits / High risk with the law / Events)
>>>> Lv 5 (Crime Empire) Blackmail (NO risk with the law / "Reputation" cost / HIGH quality girls (Nobility quality girls) )
+The morality doesn't really have to be "merged", but perhaps make maintaining both at high levels to be costly
+Evil would be more "Lusty" girls that are more easily coerced, good sex skills, but bad traits
+Good would be "chaste" girls that are difficult to crack, less sex skills but good traits
+Evil would require more "gang" involvement and money to finance the crime empire
+Good would require more sacrificing "Easy brothel" income for higher level "Legal" prostitution and money to bribe the law
Of course most of this would be "immersion" and would be played out with text-events. Perhaps more different types of morality could be modded in, similar to Plague Inc., with custom scenarios if people are dedicated enough (Incorporated with Traits: Vampire Morality / Tentacle Monster Morality / etc)
With no knowledge on programming, no clue how labor intensive these ideas are, but just thoughts thrown together
(I don't want to sound demanding lol, I just enjoy throwing out ideas)
------------------Buildings
-----Security
---------Guards
>Prevents Customer Violence
---------Snitch (Perhaps allowing several unlike the original)
>Prevents Girl Escape / Girl stealing / Rival Gang Espionage
------Brothel
----------Sex Worker
----------Matron
----------Cleaner / Janitor
----------Security
>Guard
>Snitch
>Matron
----------Cell
>Unpaid Customers
Customer family kidnapping event
Customer forced into sex slavery event
Customer takes fall for a crime event?
>Unruly girls
Automatic Cleaners
Perhaps you can tag girls for "personal training" for an event to break down the girls yourself. (Immersion)
-----Girl Interaction
--------Punish
----Remove Name (Defaults into Slut/Whore/Bitch or perhaps customizable)
----Isolation (Harsh happiness reduce / Slight Health reduce / Possible bad traits if left in too long
----Flogging (Harsh Health reduce / Harsh Happiness Reduce / Beauty Depreciation)
--------Reward
----Nickname (Defaults to Custom Nickname)
----Better Food (Higher cost / + Happiness / +Health)
----Better Room (Flat cost / +Happiness / +Obedience (If >X obedience) or -Obedience (If <X Obedience))
----Promotion (Whore (No tip/Outside) > Prostitute (Tip/Outside) > Prostitute (+Tip/Inside) > Brothel Jobs (+Tip/Inside/No Abuse chance) > Free Slave (+Wage) > Servant (++Wage/Stays in your home) > Personal Servant (No Wage / Special Missions / Doesn't work)
----If you're interested, perhaps a system to assign girls TO girls? I think that'd be fun for immersion lol
>> + Happiness -Tiredness ++Spoiled to owner
>> -Happiness/-Health/-Spirit/-Rebel/Possible to inherit traits to owned girl
>> Traits could also be added cost and benefit of this system
Maybe this could be an alternate "Breeding system" so that males don't have to be introduced yet a "family system" could be established
----Obedience System
--------Rebellion
+Chance to reject Job
--------Confidence
+Chance to trigger "Bad Events"
--------Spirit
+More Possible "Bad Events"
--------Bad events might also go through series of "skill/trait checks" for success
+=+=+=+=End Game
----Domination
-------No More Rivals
----"I am the Law"
-------100% political Influence
Perhaps the game wouldn't "Game Over", but it'd enter a "sand box" mode
Also a "NEW GAME+" option where you can bring X Gang Leaders to the new game, the starting event would be removed and you'd be directly injected into the game.
This would remove the struggle of starting a new game every major update
I can't think of much more things. Sorry that all the ideas are kind of vague and just "Thrown up" on the page. I hope some of these ideas can spark some inspiration