In fact, courts do allow that. The child doesn't have the name of either parent, so it's reasonable for the child's name to be changed to that of one parent or the other. Dad is free to suggest that the name be changed to something else (e.g., his own surname, a hyphenated name involving his surname and the mother's past or present surname), and the court would consider his petition. If dad is properly served with notice of the name change proceeding and does not object to the petition, then the mother has a good chance of prevailing under the circumstances.