Well, the Dio Brando of Part 3 has been named DIO in the videogame(s) as well as in the credits of this anime. Probably a reference to the "DIO" nameplate on his coffin at the end of Part 2/beginning of Part 3. And as far as I can remember, his full name has never been mentioned so far in Part 3.
The coffin thing isn't valid because names are usually written on coffins and tombstones in all caps, but it doesn't mean their names actually were. Joseph Joestar's name was written in all caps on his tombstone in the last episode, does that mean his name should have been JOSEPH this entire time? And I can't say I've ever heard of a need to capitalize someone's first name in English if you don't know their last name. If I meet someone and they introduce themselves to me as "Paul", I'm not going to write their name as "PAUL" until I learn their last name. The name in the credits doesn't matter either, because that's not how we write the names of characters when speaking in English. Should we all be writing 承太郎 instead of Jotaro?
The video games one is at least a legitimate piece of media that has everyone else's names in English without all caps, but Dio is all caps. Personally though, I'd just pass that off as a localization error.
In actuality, as Toni has enlightened me, the origin of this is the fact that his name is written in all caps in the original Japanese manga. Japanese people tend to use all caps when writing English because it makes the letters uniform in size compared to the Japanese characters, instead of being a mix of small and capital letters. Therefore, his name being all caps doesn't really have any significance, and it honestly looks pretty ugly.
Its DIO. The name itself deserves to be in caps. It has charm, an evil eer to it and a villainous cunning mind to obliterate peasant like you.
YOU ARE SO RIGHT OMG I HAVE SEEN THE ERROR OF MY WAYS! I hope Lord Dio... I mean Lord DIO will forgive me if I beg!