I have to say I truly don't understand wanting an invite for gmail. Why would anyone want an email service that completely invades your privacy so they can send you advertising? Yeah, they better give you a Gb of email space since they are going to fill it with spam! I'm waiting to see what lawsuits come of this.
I've never had trouble getting an email account with a good name. Well, other than when I tried to use my real name for one and was told it wasn't an allowed name...not as the email address, but actually in the name field! Go figure! I'm not allowed to have my real name.

So I gave them a fake name.

Apparently that was a better name.