You can't just change her last name, or anyone's for that matter. Even if her father relinquished his legal rights to her, your new husband would need to go through the legal process to adopt her in order for her name to change.
You have to have a "reason" to change your last name, meaning that you get married, divorced, adopted, etc.
I would ask your daughter how she feels about the ADOPTION, not the name change. If she wants your new husband to be her father (legally), then the name change is part of that process. If she does not, then it's irrelevant. My father was adopted by his stepfather at 16 and changed his name. His younger sister (13) elected to do so as well. His older brother (17) did not change his name and legally is not my grandfather's "child". In practicality he is, but he didn't have any interest in changing his name at that point in his life and my grandparents respected that.
In light of your last question, I would hold off on this whole discussion with your daughter until AFTER the wedding and the babies.