If two people have an agreed parenting plan, and one parent has not had visits in over 2 years can the parent of the child file for abandonment or sole custody, even though the parent pays child support? Also can the parent change the minor child's name ?

You can file for sole custody, but nothing is guaranteed. And no, you cannot change a child's name without both parent's consent.

As long as support is being paid, there is no abandonment.

You can try filing for sole custody, but if he's not exercizing his visitation rights, what have you really gained?