Mother doesn’t know what to do as she regrets the name she chose for her baby

This is a hard one.

Choosing a baby name can be difficult for some and easy for others. Many mums might have known what name to choose the minute they found out they were pregnant, however others don't have a clue even when the baby arrives. This mum is on the latter side of things and wrote on Mumsnet that she now regrets the name she chose for her baby. However, it's not just that she regrets the name, it's because her partner's ex claims she wanted to call her child that. She said:

"Couldn't decide on baby no2's name. Literally had 1 option in the end and went with it. The day he was born my DH's ex found out from DSC and sent abusive messages to DH saying that was the name she wanted to call DSC. "DH (and his whole family) vehemently denied this and assured me it was nonsense. "We stuck with the name and ignored it, though I was never 100 [percent] keen. Though it does suit him. "I just wish we'd called him my original choice that was dismissed early on in pregnancy. DH thinks I'm being ridiculous. I'm probably not going to change his name really thinking of the fuss it would cause.... ABIU thinking all of this?"

One user replied saying that if she wants to change the name, she has to make a decision now before it's too late:

"I think the main question is how your husband feels about changing the names. It's his child too. "Changing a child's name is much easier before 12 months, then it gets more difficult. If you're going to do it, do it now. Also, your child will begin to recognise their name, so you want to do it before this happens."

While another said that she should just keep the name:

"I wouldn't. If I changed it in those circumstances, I would always feel like I'd let his ex manipulate me into it. He's your child, you chose his name, her response is less than nothing."

What would you do in this situation?