It really doesn't matter if anyone else thinks his insistence on a name change is silly. In the time she's dated him, she could have done the change, been married and on with her life by now.
For whatever reason, he attaches some kind of significance to her having her ex-DH's last name. Maybe he has the wrong idea of her motives, maybe he just doesn't get it. But he has some kind of perception about the significance of last names, which is his prerogative..even if most people wouldn't care.
I don't see how a person can date someone for years, sleep with them (most likely), contemplate a future together, and then turn around and say it would be too much of a hassle to do a name change. Yeah, they might be a pain, but fairly insignificant in comparison to the actual relationship, and eventual marriage.
Not everything we do for people we love has to make sense to us. She would be merely inconvenienced, not harmed. It's not like he asked her to hand over her left foot.