Mom calls daughter 'oversensitive' and 'rude' for not using full first name.

'AITA for using my daughter's full first name?'

My daughter and I had an argument over her name and a friend told me to ask about it here. My daughter goes by a nickname that's a shorter version of her full first name, like Becky instead of Rebecca. (Fake name but you get the idea.)

I don't mind that she does that, but I'm getting tired of the way she corrects me when I introduce her. I use her full name because that's the name her dad and I gave her and I don't consider the nickname her real name. But when I introduce her, she'll immediately correct me like I called her a dirty word or something. Then she acts cold and distant toward me.

It's really embarrassing because whoever I'm trying to introduce her to sees her disrespecting me like that and it puts a damper on the whole mood.