Western Union would be awful to use and very costly.
We've been in business 18 years and we've always had a policy of making as many easy options as possible. If you pay by credit card it would usually say "MTGA inc." or "SMY Web inc" on your statement, so I believe that's fairly anonymous already.
We also take Bitcoin - which is completely anonymous.
We'll take cash or money orders (mailed in).
We'll take chickens, eggs, coffee, tomatoes or other good stuff :-)
Take a look how easy it can be!
http://grooby.com/paybymail.html