It’s difficult to identify with a larger group that has no name. ;–)
A small group might not have an official name, but in your mind you think of them as “my friends Timmy, Jack, ‘Batman,’ and JP”. We might hate it when other people use labels against us, but they’re important anyway. We can always expand what those labels mean if they’re too constricting or we can adopt additional labels to describe who we are. ;–)
Intersectionality is important. My identity as a proud Californian does not preclude my identifying as Gay, Asian-American, Democrat, Progressive, and cis-male. I can be all those things simultaneously as well being as clinically depressed, disabled, and poor. ;–)