I'm going to tell my girlfriend her obsession with joan crawford is weird
Why do you feel the need to talk to your girlfriend about her obsession?
Because she's been obssessing with joan crawford for a while now. She even named me after the main character from the lost weekend movie
It's understandable that you don't understand your girlfriend's interest in Joan Crawford. However, it's normal for people to be interested in and fascinated by celebrities they like. Saying this to your girlfriend may cause tension between the both of you.
I don't care and I'm going to tell her about it. I just feel uncomfortable with the fact she named me after her favorite character.
You should not make a big deal about it. Of course you can tell her how uncomfortable you feel  but no need to fight over something as small as this. There's nothing weird or wrong in being obsessive about celebrities.