Can I change my child''s last name without adoption?

I have a 4 year old son who since he was born has had my maiden last name not the biological father''s last name. The biological father left way before my son was even born and did not sign any Authentication of Paternity and the Birth Certificate. He was not even at the hospital when my son was born. I am married now I have another son and a child on the way. We all of course have my husband''s last name. Now I am all for my husband adopting my son however the time of the process is long and costly. I was wondering if there was any way I could just change my son''s last name to my married name? Since his last name right now is my maiden name I do not see why this would be a problem. I just do not know what I would need to do if I could do this. I will pay any cost just to change his name without having to go through a process of adoption. My husband and I both understand that just changing his last name gives my husband any rights over him. We just want his last name changed. Thank you.