SO'S ex wife

My significant other is divorced, has been for two years. They were married 6 years, and had no children together. She had four from a previous relationship.

We have discussed marriage, and he thinks it's ridiculous that I told him I would feel uncomfortable taking his last name. Normally, I would have no problem...

BUT, his ex wife kept his last name after they divorced. She recently sent him a pic a few months ago (explicit one), that he told her was inappropriate and she apologized.

I'd understand about the last name if they had kids or whatever, but they didnt, and I feel as if she is not moving on, even though it's been three years since they separated, and two since they've been divorced.

I just wouldn't feel comfortable taking his last name, knowing that she still has it.

Am I wrong?