Do girls like nicknames?

I've been talking to this girl for a while now. I really like her, a lot actually and every time we are together we just seem happier and people are always teasing us because we are together a lot. Today we were hanging out and I asked her if I could call her (well, lets just say, X, I don't want to say it, its corny haha). She then got a big smile on her face and looked down and said "yes, its ok". Its a cute nickname, nothing bad but by her reaction could I assume that she really did like it? If so, is it because it came from me and likes me back or do girls just like nicknames?
Do girls like nicknames?
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