How do I copyright my company name?

I think you misunderstand the purpose of copyright law, actually (though, to be honest, I'm certainly not a copyright or intellectual property lawyer, so take my comment here with a grain or two of salt). The Copyright Office explains:

"Copyright, a form of intellectual property law, protects original works of authorship including literary, dramatic, musical, and artistic works, such as poetry, novels, movies, songs, computer software, and architecture. Copyright does not protect facts, ideas, systems, or methods of operation, although it may protect the way these things are expressed."

And they also offer this:

"How do I copyright a name, title, slogan or logo? -- Copyright does not protect names, titles, slogans, or short phrases. In some cases, these things may be protected as trademarks. Contact the U.S. Patent & Trademark Office, for further information."

So let's flip over to the Patent & Trademark Office to see what they have to say about company names...

Actually, before we do, in case you don't think that the Copyright Office staff have a sense of humor, one of the questions on their FAQ is "How do I protect my sighting of Elvis?" I kid you not!

According to the USPTO (U.S. Patent & Trademark Office):

"A trademark includes any word, name, symbol, or device, or any combination used, or intended to be used, in commerce to identify and distinguish the goods of one manufacturer or seller from goods manufactured or sold by others, and to indicate the source of the goods. In short, a trademark is a brand name."

I'd recommend that you apply for a trademark for your company name, based on all this information.

Conveniently, you can fill out an application online and file it over the Internet using their Trademark Electronic Application System. You can also respond to any queries or actions from the USPTO, and file change of address notices and many other documents through TEAS.

Finally, the Trademark Applications and Registrations Retrieval database lets you dig through registered trademarks, applications, and check on the status of your own application too.

I hope that helps you get started traveling in the right direction!