If it helps any, when my chutzpah level is high enough, I can get away with following @Jilly’s
“Have you two met?”
“Does everyone here know one another?”
With
“Okay, then - I’ll start” (indicates self) “Hello, I’m $NAME”
Works better in slightly-formal (work, work-social, or club/society situations, admittedly, but does work.
(I’m also odd enough that a version of “Argh, I’m really sorry, my brain’s totally on the fritz, would you mind going round and introducing yourselves?” works - and yet I still only realised that I really couldn’t trust my facial memory a little while back.
Realising how much I did to compensate, when I did was scary.)