Please note that I am not an advocate. That said, I think that there are two questions implied in your main question and one may impact the other. When you change the name of your kid, you may need his father´s permission if he is a minor in order for the name change to be valid unless your divorce decree or settlement terms gives you the authority to do so without the father´s consent.
A change of the name of a person does not impact his/her property holdings. It is easy to understand this when you consider the case of women who get married and may have a property purchased in their maiden name before marriage. After marriage their name changes but in no way does this impact her title to the property as long as she has a proper document to prove the name change. Right? Well the same argument holds true for your son.
Just be careful that the name change document has precisely the same original name as it is in the title document and the issue of requiring father´s consent is checked. The father may later argue that he had given the property under the assumption that his name will be retained by his son but as it was not, he be returned the property. Therefore, it would be advisable to get his consent, without raising suspicion, even if not required by law.
HOPE THIS HELPS!