A customer of ours recently had a sticky situation crop up. She had set up a new website with an old domain name, and a new name for her business. After having the site up for a very short time, she was contacted by a festival promoter, who claimed that she was using their name improperly. This was a complete shock to the innkeeper, as the name wasn't an exact match, and had a few words' difference. The promoter threatened a lawsuit if the innkeeper didn't stop using the name. After speaking to an attorney, who advised that if the festival people did in fact sue, they would probably win, as they had been using the name for longer than she had, even though they did not have a trademark on the name, the innkeeper decided to find a different name for her new business. She didn't want the thought of a lawsuit hanging over her head or the possible public disdain. Using a new and different name entailed getting a new logo, updating the site with the new name and using a different domain for her website - a lot of work which had only just been done not a month previous.
The hard part about this is that even though the festival had not trademarked the name, what we understand matters legally is how long the name has been in use, and if there is a "likelihood of confusion" between the two names. If the "other" party has been using the name longer publicly than you have, what we understand is that they have the right to sue you for using the name after they started using it. They can do this while they are pursuing a trademark, and if you try to trademark the name at the same time, you more than likely will probably not succeed.
Another issue is that even if you search the Trademark Database to make sure the name isn't trademarked, it could still be in use. The only thing you can do is to search Google to see if anyone else is using the name and if so, don't use the name or contact a lawyer to see if that use is problematic. You could even trademark the name yourself if you wanted to be very safe.
This is a tricky situation. New innkeepers, especially, need to be careful. One lawsuit could close your business before it even gets started. Check your sources to make sure you aren't stepping on anyone's toes before you name your business.