Can I make it so minors don't need to put their first and last name when registering? Most of the members will be minors in my forum, anyway. There's this COPPA law here in the U.S. that won't let minors have collected information, unless their parents give them permission. But still, I don't think parents would let their child join a forum that asks for that kind info.

no way.
Kids should always follow their parents' advices.

No forum for kids.

why not, they can register anyway

This is for kids under 13
This is a law in the United States

But kids over 13 can register

I think you should read at this website and show it at yours parents
http://www.ftc.gov/bcp/conline/edcams/kidzprivacy/kidz.htm

But I wonder how many minors put gibberish instead of true info when they are required to submit personal info to a website.

This is their problem !
The admin can't be responsable for kids that lied about the age ...
Parents should be careful of what kids are doing on the internet ...
Because it don't concern kids over 13 ...
And before this age, they are very curious and don't think of consequences and try to click anywhere ...
Parents should have a look, maybe not stay always watching what kis are doing ...
But if a 11years old child use internet, without know what they say, parents should ask for information :
Just for instance to know, ok this is a RPG about Harry Potter, and they shoud try to be interested : "Can you show me how it's work?"
Before 15 or 16, children usually repond easily to those question and would be glad to explains rules to their parents ...