Ok, so firstly, and very respectfully.... Let me quote Ronald Reagan.... 'just say no'. But that horse has bolted. If you didn't want the name changed you should have just said NO.... But I also understand why you may have succumbed to the bullying....
What to do with gifts? put the first name. Nothing else. No last name...
OR
Suck it up (again, sorry and very respectfully) Trust me I get it... But you signed the form. And put the kid's hypenated name on the present. What matters more, Oooh. I get to quote shakespeare... "A rose by any other name smells as sweet". U'm it come from Romeo and Juliet, both of whom wind up dead at the end.... Make of that what you will.... I reckon this is your best option.... for two reason. 1- the kid will get the present. 2- You're arguing with a fool, you know your ex is a fool right? Anyone who would deprive their kid of a present from their dad for this reason is a fool.... BUT when you argue with a fool.... Well, it is a foolish thing to do and that makes you a fool.... Again, respectfully....
OR
Apply to court to have the hyphenated name changed back. But, you wont win and you will spend a small fortune trying.
Final thought - mate - this is a law forum. So you have nothing as far as the law goes.... But some friendly advice, not legal, just life experience..... Learn to make sure this stuff doesn't get to you... So from my experience with a nasty vindictive ex I am learning (and it is bloody hard work) but I am trying to not let this sort of crazy stuff get to me. I'm learning slowly and I'm far from zen budda perfect, but the stress is bad news. It will cause you to die younger than you should.... My mission is to be around long enough to be a grand parent, do the best for my kids and dance on the ex's grave with my walking stick.