I know that usually we do not translate names, but how would you translate Indiana Jones into Latin?
According to Wikipedia, Jones is literally John's son in Welsh, and it's related to Latin Ioannes and Iohannes.
Latin Language Stack Exchange is a question and answer site for linguists, teachers, and students wanting to discuss the finer points of the Latin language. It only takes a minute to sign up.Sign up to join this community
Perhaps surprisingly, "Indiana" is already Latin! It comes from something like terra Indiāna, "Indian territory", because when it was first colonized it had a larger Native American population than any of the surrounding states. So you could either keep that the same, or put it into the masculine (meaning "the Indian man"), Indiānus.
"Jones" is a patronymic, as you mention, meaning "son of John". Classical Latin didn't really do patronymics, but Greek did, so an educated Roman would certainly recognize them. One method was to just put the father's name in the genitive, which would be Jōannis. Another method, the fancier/more poetic one, was to use the suffix -idēs, giving Jōannidēs.
I would translate Indiana Jones to Latin as Indiana Jones. This is common practice in contemporary Latin: names are used as such, and sometimes given names are Latinized slightly. Here the given name Indiana — which was not actually the name given to the character as we learn in the movie Last Crusade — fits Latin language perfectly and no adaptation is needed. It is not an issue that a male's name looks like a first declension feminine, and such names existed in ancient Rome too.
If you want more justification, there is a classical Latin precedent for this. The Romans wrote about a number of Greeks but they were (almost?) always called with their Greek names. They were transliterated to the different alphabet and the endings might have been Latinized (from -os to -us, for example), but the names were not translated. Many Greek names mean something and the Romans did know enough Greek to form Latin versions if they wanted to. But they didn't; names were kept mostly intact.
Of course one could translate or adapt a number of names to be fully Latin, but I don't think that's a good idea here. My own last name is a meaningful Finnish word, but I still use the name Ionas Ilmavirta in Latin; my first name is a Finnish variant of something of Biblical origin, but translating the last name would make it very hard for people to connect my actual name to the Latin one. After all, I do use the same name in all languages.