Trademark rights are based upon usage not registration. This means that you don't own a trademark by selecting the name or brand. You own a trademark because you use the name or brand. To see if you can register a mark you need to find out if anyone else has the right to the mark.
United States Trademark Office Search-Structured Search
The first place to see if someone owns your name or brand is to see if anyone has registered th3 trademark or attempted to register the mark. The USPTO has a se…