Go to www.uspto.gov and conduct a trademark search of the name you'd like to use. If anything comes up in the search results, review the results and determine if there are any that are in the same or a similar class or category as your product would be in. For example, if your business is making chocolate truffles and the potential name you'd like comes up in the search as being owned by someone in the candy industry, you'll need to pick a different name. But, if it comes up as being in a category for selling tires, then it might still be available. No one's going to walk into a tire store wanting to buy chocolates and vice versa. The standard is if the potential trademark would be confusingly similar to the consumer. If you are unsure if the categories are similar, consult an attorney to help you evaluate it.
Search state trademark databases
If you will be operating in all 50 states, it's best to search all 50 state trademark databases. The searches will be similar to that on the USPTO website.
Do a Google Search
The previous 2 steps will help you determine if there are any registered trademarks that would potentially conflict with your proposed name. But, that doesn't reveal any potentially conflicting common law trademarks. So, do a Google search for your proposed name, putting the name in quotes. You will need to determine if any of the results are product names or businesses on which your proposed name might infringe. Again, the standard is whether it would be confusingly similar to the average consumer. If you are unsure, consult an attorney experienced in trademark law to help you.
Do an Online Yellow Pages or Anywho Search
The Google search above will reveal any potential conflicts of businesses that have websites, have issued press releases, or have been mentioned on a website. However, that won't help with some of the small businesses that aren't on the web and just have a brick and mortar business. So, you'll need to search the yellow pages or similar type site. If you are going to operate your business on the web, you'll need to conduct this search in all 50 states. If you are only going to be operating in one state, do the search in just this state (although, I'd recommend all 50 states so you know what is out there).
These searches won't guarantee that there is nothing out there on which your proposed name will infringe (not sure anyone can really make that guarantee). But, it will get you as close as you can without hiring a search firm to conduct the searches for you. Good luck with your searches and I hope your new business is very successful!
Additional resources provided by the author
Disclaimer: This answer does not create an attorney-client relationship and does not constitute legal advice. Each situation is fact specific and there may be facts not disclosed that could alter the answer provided. It is impossible to evaluate a legal problem without a comprehensive review of all the facts or documents.