My ex is calling his new gf the same pet name as he used to call me?

I just heard that my ex ( we were together 6 years ) is using the same pet name he used to call me. I have been told that he is saying it most all the time to her and is even bringing her to the our favourite places where we used to go often. I have remained 'friends' with him ( we were friends before we went out ) but since he has met this girl and went into a relationship 2 weeks after he met her, he has not been in contact with me but only once to chat for 15 mins to tell me he was no longer single... Before he was on most everyday chatting, texting or we would chat over the phone. Now all quiet. It is like I do not exist any more.

Thing is, I would not call a new bf, the same pet name I had for him. So why not give her a different name? Why use the one he had for me?

What would you think? What would you do if you heard or saw that your ex call his or her new partner the name he/she called you? How would it make you feel?

He had told me before that that was my name and it was me. Now I hear he is using it for her.