I remember watching Voyager for the first time on it's UK premiere on Sky (with spoilerific 10 second clips from later in the episode played at the start and end of commercials because screw the viewers) and going "oh, it's that guy from the Next Gen academy episode!" and maintaining that belief for many years until I rewatched TNG and the fella's name was Nicholas Locarno and not Tom Paris. The real life reason was not to have to pay the writer of "The First Duty" for every subsequent appearance of the character, and the Voyager series bible even had a slightly different version of "The First Duty" backstory made for Paris even though early drafts literally had him listed as Locarno
I also assumed these were the same guy too, but according to the novels (and one of the Voyager writers) they're actually identical twins Taurik and Vorik.
In one of the most famous examples, T'Pol from Star Trek: Enterprise was originally going to be T'Pau from "Amok Time", but again not wanting to spend royalties every episode had her morph into a new character. And a young T'Pau would eventually appear in season four.