It really is all about your feelings, because it is YOUR name, and they were YOUR biological parents.
I helped the third ex with a slightly different situation. He was born out of wedlock, his mother married his step-father, and concealed from him that he was not the step-father's child. The step-father never adopted him, and he found out by accident that all of his school records were under his step-father's name, but his birth record was not. He went to the registry of motor vehicles to get his driver's license, and no one could find his birth record.
He went to his mother to try to find out why, and she never did answer him. She just burst into tears. Her shame was apparently far greater than her love for anyone but herself.
I have never seen anything mess up anyone's head the way it messed with his, thinking that everyone he knew and loved had lied to him all his life, and I guided him through the process of legally changing his name to that of his step-father...who was actually nasty enough to be suspicious about his step-son's motives...at first.
I have kept that last name, so I think of it often.