Yes I would
In my opinion it means she's not 100% committed to you and the partnership between you two.
Others will say that's not the case but if not then what would be the big deal to change her name if you're everything to her?
Or she could use both last names if she doesn't have a middle name or substitute with it.
Ownership of women has been a popular priority in many cultures for centuries.
My first wife took my last name and has never changed it in the 24 years since our divorce
My current wife of course kept her last name and I approve as it gives me an in with the Tribe when their world domination is finally achieved