Can a parent change their kid's last name if the father has had no contact in over 3 years?

My son married a woman a year ago, and she has yet to change her name from her previous marriage. She doesn’t want it to be a different name from her son, Jayden. I totally relate. When Rick asked me to marry him I told my son, who was 18 at the time, that I was fretting over changing my name.
He said, “You mean we can’t call you “Mom” anymore?” Totally made me laugh and relax!
So, my son is kind of upset over this and I sorta see his point.
Now, he wants to adopt Jayden, but it’s an expensive process and they just don’t have the funds to do it right now. Plus, they’d have to hire a lawyer to prove abandonment on the part of Jayden’s father to get his parental rights terminated. He doesn’t pay child support, either.

So, is there a way to change Jayden’s last name that doesn’t require all kinds of legal maneuvering and expense?