Now, generally a parent would need to consent of the other parent in order to have a child's name legally changed.

If the parent seeking the name change already has court ordered full legal and physical custody, does this rule still apply?

Yes the rule applies. Here is why. The other parent still retains some rights to the child. If they had no rights whatsoever then you would also be stripping the child of their right to parental inheritance ( a legal claim ) not an entitlement. That's why we talk so much about TPR's. After a TPR there is no claim nor rights whatsoever. All legal does is grant you the decision making powers.. Physical grants you time with the child. Should something happen then your ex would be first in line for custody of the child / children. Only a TPR removes that right.

If they had no rights whatsoever then you would also be stripping the child of thier right to parental inheritence

Oddly enough I just researched NC law for a different thread. NC law specifically states that all rights AND obligations EXCEPT for the right of inheritance are terminated with a TPR.

So, in at least that one state, a TPR does not end inheritance, but an adoption does.

Oddly enough I just researched NC law for a different thread. NC law specifically states that all rights AND obligations EXCEPT for the right of inheritance are terminated with a TPR.

So, in at least that one state, a TPR does not end inheritance, but an adoption does.

Your right that is odd because it was my belief that a TPR was a severence from the relationship in all ways.