"Veni Vidi Veni" would be a great name for a strip club or brothel.

What is even a roman-themed brothel? Is that just an excuse for AIDS?

Why would the sex be unsafe? There are Trojans everywhere.
- Nah, Trojans only hang out at Greasey places
Well, people present could wear some sort of short attire for easy access...

It should be more transactional.

Vendi, vidi, veni

(Technically it should be Emi, vidi, perveni)

I laughed too hard at this. Thanks!

"I arrived, I saw, I arrived"?

Why?

I came, i saw, i came.
- This is a bad translation because the English word "to come" has a double meaning (it also means ejaculation or having an orgasm), while in Latin it doesn't. There's a big risk of a misunderstanding, so "I arrived" is a much better translation IMO.
  Why do you think "I came" would be better? 🙃
"I came, I saw, I came"
- I'll copypaste this thing I wrote under another comment:
  This is a bad translation because the English word "to come" has a double meaning (it also means ejaculation or having an orgasm), while in Latin it doesn't. There's a big risk of a misunderstanding, so "I arrived" is a much better translation IMO.
  Why do you think "I came" would be better? 🙃
Vine, vi, me vine
I don't know how does it hold in italian, but in spanish kind of still works. Nevertheless, In spanish "venirse" isn't that common for came.. well, at least not where I live. Acabar, correrse.
Any Italian friend in the comments that can bring some light into the matter?

"Ever since the city of Rome opened the 'Veni Vidi Veni' gentlemen's club last month, tourism has increase sixty-nine fold."

That wouldn't work in Latin (were the correct translation to give the meaning you want would be something like Veni, Vidi, Eiaculatus), but it kinda works for english-speakers who also know enough Latin to get it, though I suspect most don't.

Next to none of us know Latin, but we pretty much all know "I came I saw I conquered"
- Well, as I pointed out somewhere else, suggesting "I came, I saw, I came" in English as the name of a strip club or whorehouse is by itself pretty much the whole joke, and people don't need to know Latin to get it (to get "Veni, Vidi, Veni" one needs to know both the original expression in Latin and that the word "Veni" means "(I) came"), exactly because as you say, pretty much everybody knows "I came, I saw, I conquered".
  Putting it in Latin for me feels more like a way to signal one's above average educational or cultural level, that anything that enhances the joke.

the 'veni' usually comes last, tho.

Right, which is why it's there at the end.

I doubt there is a lot of overlap between people who go to strip clubs and those who’ll get the reference.

I have a pretty good idea what you were doing in the shower, when that particular thought occurred to you.