My question involves name change laws in the State of: Tennessee

Ok when my 2 year old child was born i was married to my ex husband and he was not there to sign and did not sign her birth certificate but he is on it anyway and her real father (my husband now) wants to be the one named and have her named changed to his. But the man named on the birth certificated wants a DNA test and my husband (the father) don't want to put our child or himself through all that. What does the Tennessee state law state about this.