So the man on my daughter's birth certificate isn't the biological father and left us due to no longer being able to handle the stress. I want to be able to have my daughter have my last name instead of his due to not having him in either of our lives anymore. My daughter is only 15 months old, so she doesn't understand that he was her "dad" but I know he isn't the biological dad and he also knew that as well. If someone has answers or any kind of information for me that would be great. Apparently I need a form signed by him signing her over to me, but I am only 21 and don't know enough about all of this. Any kind of help would be amazing, thanks.

If the many on the birth certificate acknowledged paternity he is the legal father and responsible for the child. You would, therefore, need his permission to for a court to change her name. There is no form for him to sign since he can't give up his rights. Only a court can take those rights away and it is unlikely they will do so.

He may not be the bio dad, but legally he is the dad and on the birth certificate. He will be the one that the government goes after for child support if you receive any government assistance.

So if your location allows, you are going to have to challenge his paternity in court to get full custody of the child.
Some locations may not even allow that, since some areas have strict rules about a "legal" father.

Also remember that by admitting you both did this, it is a serious fraud that was done. And there is some man, who is really the bio father who has lost or been denied his legal rights to the child.

So you may even have to attempt to find the real bio father to be allowed to change the child's name after you get the legal father off the birth certificate