Can I change the last name of my son from my first marriage (who's father has no rights to him) to my second husbands name without my second husbands consent?

What? You want to change your son's last name to your husband's last name without your husband's consent? Do I have that right? Why would you be so deceptive? Changing his name (if that's what you are thinking) to force him to pay support at some time or other is not going to work.

What does his father has no rights to him mean?

This is too late for a Father's Day gift, so your reasons are important.

But you don't need your second husband's consent. However, unless your first husband had his rights terminated he may have some say in the matter.

First you can not change it without notifying him and trying to get his permission first.

I will say you need to explain has no rights ? Have you already went to court had had his rights taken away, or has he just never went to court to get visits and other rights ?