It's definitely a nickname given to him in the CIA, yeah (and, since this is MCU, it's even odds the people who gave it to him were actually Hydra...) And from Ross, you get the idea that it wasn't used as a surname or epithet, they just plain called him "the Killmonger".

I've only seen the movie once, though, and I can't remember if Klaue ever addresses him as anything? I'm thinking not, though, I don't think we got the Killmonger reveal until Ross said it, and that was after. So in the movieverse he's never called "Erik Killmonger" anywhere but the credits.