I was given by my biological father to his sister and her husband but there was no adoption papers involved. I still carry my mother and father's biological name (I'm also an illegitimate child). I'm of legal age and decided I want to change my last name to my adoptive father's name. I know that isn't much of an issue, but I also intend to merge the last name of my biological mother and adoptive mother to be taken as my middle name. Is that possible?

Yep, a basic fill in the blank form at the court house ( probate court where I am at) but various courts around the US ( different states use different names) but you fill out the form, file it, pay a small fee, and the judge reviews it latter, signs it and that is all there is. In most cases there is not even a court appearance, but could be one required in some states

Can a man change his first and last name even if he has been convicted of a felony?