When naming your business, it's important to check the public records to be sure there isn't any other business already using the name.
I received a call today from a client who wanted to use the plural version of a name already in use for the exact same business. In support of his using the name, he said that the city business license bureau was willing to issue him a license.
Licensing bureaus are only too happy to take your money and issue you a license. It's not their job to check to see if the name is already in use. In fact, if you end up getting a license under a name already in use, the first company can come after you for infringing on their name.
I suppose I should clarify - you don't have to actually register a trademark in order to have some protection against someone else using it. You only have to use it in "commerce," which means you actually have to use it in conducting your business, and you have some protection. Granted, registering it does provide additional protection. See "Should I Register My Mark?"
Finally, you cannot steal a name from someone already using it by registering it. Simply by virtue of using the name in commerce, they have established intellectual property rights in the name. Any attempt to steal it will most likely trigger a lawsuit.
How do you know if the name you want is already taken? Google it first. Then check the business license bureaus, the Secretary of State, and the county DBA database. Here are some links:
City of Las Vegas
City of North Las Vegas
City of Henderson
Boulder City
Clark County, Nevada
Nevada Secretary of State