I'm not going to tell my girlfriend the name of an old friend
Why wouldn't you tell her the name of your old friend?
She knows this person and I don't want to upset her or have a fight.
Well, it is important to be open and honest in a relationship.  But, if you think this would truly cause her upset and it really doesn't matter if she knows or not, then skip it.
I don't want to tell her or talk about it.
If you think it is best not to tell your girlfriend about the old friend, then you should do that. No need to stir things up.