Ok, my son has both of our last names on his birth certificate and ssn. The thing is that his father vanished from our lives since my son was 2 years old and he's 7 Nd. Half. He remembers his dad but only knows his dad to be my fiancé who h met his when he was 2 years old. My question is, since the biological father disappeared and to top it of he's illegal in USA. Can I remove his name and only keep my last name instead of my son having two? He's been saying he wants to have my last name because my whole family and his little brother even me n my fiancé have the same last name so he feels left out :( let me know what I can do?

It will be up to the laws of the area where you live. But in most places you will have to get the fathers permission or at least attempt to find him and notify him.