What are the possible causes where a judge will allow a name change for a 5 Year old child?

My son's father named him at birth. He was around until 9 months and has not seen him since. I have sole legal and physical custody and I am in and out of court on contempt for child support and modifications. To date, he owes over 23,000 dollars. Last week, I received a letter from him with a fully competition name change petition he completed for me. His letter stated I should sign the form and return it to him to make this name change easy for him. I have no intentions on changing his name nor have we ever had a conversation about it. My son is able to write and spell his name. His modeling contracts, website, and other accounts, are all tied to his name. His father's actions are out of spite and I want to know what chances he has and under what circumstances will a judge change the birth name of a child. I have sent him several cease and desist letters, filed for a protection order which was denied and now this. He has called the FBI on me with false allegations, changed to 6 figure job to a minimum wage jobs to avoid his child support payments, called the daycare provider telling her lies and garbage. Now he is using the law to harass me.