as far as Tommy giving out his and Joel's names, Joel already yells out Tommy's name during their fight in the ski lift thing (at about 5 minutes), so it's not like giving out fake names wouldn't have tipped Abby off afterwards.
https://m.youtube.com/watch?v=4X1YJXxlcwo
and in the situation that they were in, it made sense for Joel to yell out to Tommy to specify that he wasn't calling out to Abby (plus, they likely felt there was a good chance they weren't making it out of that situation.
finally, when people say it was out of Joel's character to trust people with his name or trust himself to be around Abby's friends like that, he already fought with a stranger who he ended up trusting his and Ellie's lives to in the first game - Henry.
"I could never encapsulate all my cosmicality on my own."
- mr. MFN eXquire. https://imgur.com/a/CwuPnzk