My son is two years old and his dad hasn't been around since he was a month old his dad contacted me recently and wants to give up his paternal rights to him and have the baby's last name changed which is completely fine with me I would love nothing more than to do this. How can we go about this?

Depends on what nation you live in, In the US, you can't, a man can not just "give up his rights" and of course he would still have to pay child support ** I assume he wants to stop paying child support as the reason to give up rights.

After you get married again, and your new husband wants to adopt the child, then he can sign over rights to allow the adoption.

Is he paying child support at this time? Why does he want to sign his rights away?

There is a myth that a parent can just sign away their rights to a child. But in much of the world (and definitely in the US) its just a myth. Any question on law needs to include your general locale as laws vary by area.

So the father is probably laboring under an incorrect assumption that he can do this. Its unlikely that he can. Unless there is a step father who wants to adopt, this is unlikely to happen.

However, if you want to change the child's name and he doesn't object, you can file a petition in your local court and that will be granted.