Possibly, but it wouldn't have the benefit of being 100% legal, as voidnull's solution appears to be. Also if Wordpress were to discover your fake info they might take your site down.

However, because you can't delete your Wordpress.com account http://www.accountkiller.com/en/delete-wordpress-account && http://tosdr.org/#wordpress-com providing false information is the only viable option in case you want to get rid of it.

Why is that not 100% legal?

Providing false information to WordPress is probably not legal.

This is what I had in mind; good old CFAA. Ditto for entering false info in moneygram. (Not commenting on whether these things should be illegal.)

Well, it also touches on fraud and impersonation, old, long established crimes, not just computer hacking.

Is laundering legal money and then using it for legal purposes illegal?

If the money was obtained legally to begin with, concealing the source is not illegal.

http://www.law.cornell.edu/uscode/text/18/1957

Giving them fake information would be illegal and probably be breaching their ToS.

I can see this breaching their ToS and would probably be shut down by them if brought to their attention. However, what law would you be breaking when you give a private company a fake name.

Regretably, in the US the "Computer Fraud and Abuse Act" (CFAA) makes it illegal to access a computer without "authorization". Courts have interpreted that to mean that accessing a site when you are in violation of their terms and conditions (for instance, with a fake name) is a violation of this law and thus a felony. Learn more: https://www.eff.org/ja/issues/cfaa

New question: does it matter if it's illegal if it's 1) moral and 2) you're anonymous?

If its illegal, then it's much more likely to be shut down. Do you want to release some information once off, or do you want a reliable Web host.