My guy doesn't call me by my name, what does that mean?

So he used a nickname that was poetic it was really nice but I felt like a stranger for him and I asked him to please call me by my original name but he never used it once after we talked about it.

So I just yesterday I had to ask him again and he said that he would but I'm not sure what his feelings are. I feel that he finds my name appealing but he may feel over possessive about it.

At the end of a conversation he just say "your mine".

My guy doesn't call me by my name, what does that mean?
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