This is the first time anyone's explained anything like this to me. It's possible other game developers are in the same boat as me, not knowing. I know of trans dysphoria thanks to a few helpful people on the discord server explaining it to me. This topic never came up though.
I can't guarantee anything but if I were to change around the words, could I get a bit of a ... umm... I want to say guide? but I don't think that's the right word... But like how previously people have helped me understand the past tense/present tense of they/them. Could I get a few replacement word options?
Vagina/pussy = ???
Pussy lips/slit = ???
Clit/bean = ???
as well as:
Penis/dick/cock = ???
Tip/head = ???
Balls = ???
Again I can't guarantee anything as it's a lot to go over and it might not work out sentence structure wise, but I can always try to include such things moving forward. The reason for this is cause in the code it's kind of like a madlib situation where words are just replaced instead of the entire sentence.
Does this dysphoria also include when a character is talking about their own body parts? Or just the pov situation?
Like I said, this is absolutely not anything I think is a mistake on your part - so it’s okay if it’s difficult/impossible to implement or hard to understand. I appreciate that you’re willing to try.
I can only speak for myself in terms of what I find acceptable, but here are some word suggestions (others may find these off-putting):
Vagina/pussy: hole, front hole, cunt (some may not like this one), boypussy/boycunt (another that some may dislike), man cave (kind of hokey)
Pussy lips/slit: lips, folds, vulva (might be too anatomical-sounding?)
Clit/bean: dick/cock, t-dick/cock, dicklet (can be used to humiliate also, if that’s relevant), nub (kind of vague but gets the job done)
For terms referring to a trans woman’s genitals, I can’t say what a trans woman might prefer since I’m not one, but here are some terms I’ve read online:
Penis/dick/cock: dick/cock (some trans women don’t care about terms that much), shaft, strap, girldick/girlcock, clit, member, hen (like a cock but for a girl lol, uncommon but catching on a bit), venus (penis but with a V, also uncommon)
Tip/head: I’m not sure if there is a specific term that trans women might prefer for this part, tbh
Balls: Again, another one I’m not sure of, but I’ve read people online sometimes use “orbs”; more info/opinions from trans women are probably needed
In general, I’ve also read that a lot of people use the words “bits” or “junk” to refer to essentially any aspect of their genitals, but that seems a bit non-specific for an erotic role-playing game.
Regarding your question: “Does this dysphoria also include when a character is talking about their own body parts? Or just the pov situation?” I would say yes - it’s pretty difficult for me to refer to my own body using conventional terms, even through text.
I totally get that this may not be possible/practical for you to do! That’s totally okay, I’m fine with a game not being tailored to me - they are a lot of work to make and you’re a solo dev. Again, I really appreciate your efforts to understand and see if this is workable. Thank you for having an open mind.
Here are some word suggestions (for referring to a trans man's genitalia) from me as well (in case they're still needed):
"Vagina/Pussy"= (front) hole, things with man or boy in front of them like mancunt or boypussy, just cunt is also fine (but just "pussy" is pretty iffy for me personally, better with man- or boy- in front of it)
"Pussy lips/slit"= honestly have nothing for that, since I never use that part of my body. Also a tip: would be cool for people with two holes to have the opportunity to only use one, since I'm one of those people that can't use the front (for reasons of dysphoria and physical discomfort) and only do anal.
"Clit/bean"= dick, cock (there are a few more but those are the ones I use and I see other trans men use most of the time)
Are you on the discord by chance? I felt like taking on the challenge and created ... well I'm not sure what to call it haha, but it's a OH! I can attach pictures! I wanted to show you afterwards but I wasn't sure. but picture comments change that! 
My menu art hasn't been updated yet to incorporate the word dysphoria option, that's a task for later but it's in. It changes the name of these words regardless of who owns the body part. (I think) I didn't quite understand if the dysphoria is only in reference to the body in possession or all bodies. (Not sure if I'm making sense there)
I added a Male and Female button at the bottom (which I need to change to genitalia names cause gender =/= genital's (I derped on that one, I threw it in there fast)) but I added the feature to change all words based on body part, cause again I didn't know if it was just pov's body or all bodies? So, if you're sex is the opposite of a characters and you want to edit what words they use to refer to themselves then you can.
The only down side which I haven't manage to figure out how to fix is, it doesn't change it in the game right away. Like if the word is in the line you paused on to go change it, it won't update that word, but it will update all to come.
Usually dysphoria-inducing words are in reference to oneself and not others. So if I heard someone use the word "clit" in reference to a woman I wouldn't care (but if it were in reference to a trans man I would care, unless it was clear that he was okay with other people calling it that). So as long as all characters are cis, I don't think it matters.
But I'm really happy that you care enough to implement the option to change those words! I've played other (erotic) games where "genitals don't equal gender" but they still use the same words and even call it a "female/feminine climax" or some shit sometimes. So as a trans man who's always had to either regret making a trans male character because of the words that are used or roleplay as a cis man and feel either dysphoric or completely disconnected when balls and ejaculation are mentioned I can't tell you how much this is appreciated!
And I'm not on the Discord, I am in two Discord groups for erotic audio creators but only use them to listen to audios they can't put on Patreon, so I never interact otherwise. But if there is other relevant (mostly trans-related, I guess) discussion for this game then I would probably join in.