I don't know how long you have known this woman - has she always been like this? I would feel stifled if she was my friend. You spoke to her about you upset over name thing and she didn't stop. That's not at all friendly - quite the opposite. To me, it seems she is doing these things for her, not for you.
It reminds me of a friend I had years ago when I was pregnant with my first son. I hadn't known her long but she was very keen to see me throughout my pregnancy and became quite protective. She visited me tons of times at the hosptital and it began to veer from her being attentive to her being in the way. She was trying to take over everything and questioned all dh's decisions.
She had no children of her own, and this might well have been a factor in her extreme interest in my pregnancy.
Anyway I began to distance myself from her a little while trying to be friendly still. But once she sensed what I was doing, she turned on me very quickly and immediately became a different person. Dh and I had loaned her furniture for her new flat and a year afterwards I politely asked for it back - she laughed in my face and said that she'd given it all away.