I would like to copyright my companys name. How do I do it?

First thing first you would not copyright your company's name that would be a trademark. Copyright's are for published and unpublished works, people get it confused all the time. There's the cheap way to cover yourself and the extra cheap way to cover yourself. If you are already in business and have a business license you can use that establish your right to name use. The key to that is making sure the name you want to use is not already in use. If you are challenged you have proof of how long you have been in using the name the guy who was first has the rights. Do not I repeat do not pay someone to trademark your name (ie lawyer) its too easy just to go on the patent and trademark site yourself and do it. That paying someone to do it is a hustle some intern will probably file that paperwork anyway and you'll be out thousands!!! You can also do a trademark search on uspto site which is neat for find out when a brand got started