You have the right to change your name. Your mother has the right to not like that, but that's not your problem. As you say, it's not even your mother's name, so I don't see where this is some legitimate source of distress for her.

Do what feels right to you. At some point, like after the change is fianalized legally, you might do well to say, "Mom, the subject is closed. I'm sorry you feel unhappy about this, but I'm not going to discuss it further." Then do not be drawn into defending your decision. She'll get over it. If not, then she needs to get a life . . . one that doesn't revolve around causing turmoil over what has utterly zero impact on anything of importance in her world.

That last point begs the question of what this is really about. Does she have a hard time seeing you make decisions independently without getting approval from her? If so, then this is exactly the kind of experience she needs to have more of. And so do you. If your father was abusive, this name change may be very good for your soul. Now that's important.