People only have one name in a name. If your name is Chaim Berel then it's "Chaimberel" not two separate names Chaim and Berel. I don't have any proof besides for that we say וקרא שמו and not שמותיו.
You can have multiple names like Moshe or yisro (even that, could be it's a nickname but that's not mistaber) but not two names in one.