As you know your company name only gives you a license, not a property interest in a name.
People will file their trademarks alone, however it is a perilous process.
The United States Patent and Trademark Office (USPTO) website has a lot of information on it about trademarks, however it is a bit more complex than just searching the trademarks register in the US.
There are other searches to conduct apart from the register and any pending applications which might reveal a potential problem with your future trademark. For instance a common law search of many different resources is recommended.
It also depends on your strategy and whether you wish to register your trademark only within the US or in other countries, whether it has a design/copyright aspect to it, and whether there are any domain name issues.
We are living in a global borderless world on the internet whereas trademarks are territorial in nature, so it would be worth the investment to find a Trademark Attorney whether by private referral or through your State law society.
Start with your State's Department of Licensing - start with a state trademark. Then contact the US Patent Office - go to their website and look up copyright/trademark laws. It's all pretty easy and just requires forms and minimal expense.
You can try to do it yourself by going to this web site: USPTO
However, most attorneys don't recommend to do it on your own because it's relatively cheap to do it using a qualified lawyer (a few hundred bucks, if there are no major issues) ..... and if you do something wrong, it will make the whole registration process much longer.
I hope that helps.