I wouldn't change it. I would be skeptical as to why it's "very important" to the new husband that you use his name. That's such an odd thing to say. "Very important" seems to imply ownership to me. And you've got a fairly long and established career going...seems silly to change your name now.
Our birth surnames do often come from our fathers, and I can understand not wanting to honor a difficult or absent father, but at some point we need to just embrace who we are now, and not think of it in patriarchal terms. I use my birth name, but it's my name, not just my father's. I gave it to my children too. I had to start somewhere.