Harry Wombat
I wouldn't argue with anyone or come off sounding like a "freeman" in any way, shape, or form. They might call Family Services, security, police etc. if you argue and try to explain your position any further. I'd just play the role of concerned diligent parent that has his priorities straight and insists on discussing such matters with your lawyer. Get yourself, your child, and your mate home safe and sound. Off the top of my head - I'd tell them:
1, You and your mate are presently undecided about the name and won't be rushed. It's a serious decision and you'll need more time. You want to consult with and get more family input.
2, Because you are prudent you will obviously want to consult with your lawyer (wink) before signing - to discuss the full legal ramifications of any forms or paperwork they (or anyone else) may want signed. Ask for a few copies to take with you. Let them know that attending to the baby and mom is the first priority of course - and you'll likely speak with a lawyer within the next few weeks or so when everyone is well rested again and all are thriving. ;)
3. I'd inquire if their legal team would be so kind to provide any information they may have in writing, providing full disclosure and explaining their position concerning what they want you to sign and you'll be sure forward it to your lawyer for their consideration, whenever you get it in the mail.
Congrats Jesse.