Name change because parent not visiting child

I have the sole physical custody of my minor child with the father
having the usual visitaion rights. I am a citizen of state of Georgia.
The father does provide child support. But he refuses to have any
relationship with his son. In these circumstances, it is very traumatic
for my child to bear his father's last name when he has never seen him.
Can I change his last name to my last name without the father's
approval. Since the father hasn't visited my child in over an year, can
this be considered abandonment. And can abandonment be a reason enough
for me to file for name change of my son. At the same time I do no want
to lose child support. Please suggest avenues for his name change.
Thanks in advance.