I have a moment of sheer panic that I'm not going to remember my friend's names every time I'm introducing someone to my friends.
Have you always had this problem?
No, it's only been happening for the last couple of years.
It's a bit odd to panic in typical everyday situations. You should learn to get over this fear.
I'm wondering how to hide my panic and not come off as a massive mental case.
I think that worrying about hiding your panic may just add to your stress about this. Perhaps you should look into the root of these feelings so that you can resolve them.