My nine year old daughter carries my last name and wants to legally change it to include both of her parents last names. A recent change of law where we live makes this possible. The other parent and I are separated and they also want this change.

Am I the the asshole for having refused to sign the name change application during a year or two and not wanting to sign it until she gets older? I have no rational argument for this decision, some vague feeling she's too young but I can't say that I believe it would hurt her, even if she would regret the decision later on.
This example is WRONG.