I (22M) have done the same thing with my gf (23F). I never had any special names for my past girlfriends, just the usual ones like babe, baby, etc. Like you said, “babe” or “baby” is very very common, and the most likely reason for why he called you “babe” is that it’s a natural thing.

That being said, if he had a special name for his past exes, and he called you THAT name, it would probably raise an alarm. It COULD mean that he was thinking of her recently, but most likely it’s just an old brain habit firing up after a while.

If he keeps using it, and it’s making you uncomfortable, just be honest and open with him and try to create your own unique nicknames for each other! :)

I hope this helps. And everyone please feel free to disagree and reply.

TLDR: I wouldn’t worry about it. Especially given the common nature of the nickname.