Nintendo Dream magazine had a chance to talk to some of the dev team behind Fire Emblem: Three Houses, and they asked them all sorts of questions. At one point during the internet, a discussion of Claude comes up. That's when Intelligent Systems' Toshiyuki Kusakihara reveals that Claude is actually a fake name. Check out a translation of the reveal below, courtesy of Oni Dino.
Claude’s real name is “Khalid”. I wanted to include it somewhere in the game but there wasn’t really a good opportunity, so here we are (laughs). We actually had a scene about halfway in where Nader calls him by the name “Khalid”, but we couldn’t find a good place for it to fit so we ended up cutting it. ...the name was originally intended to be an alias, so I didn’t worry about the overlap in names. I always wanted to reveal his identity during the game, but… Oh, well. There’s other characters throughout the series whose names overlap with each other, so I’m not bothered by it. Anyway, his real name is “Khalid”!