Hello I am a licensed attorney. I am here to help answer your questions. Please do not hesitate to ask for clarification
The employee is stating you should trademark the store name?
If you want to protect the saying from being stolen by competitors,
you can trademark the saying to protect it,
However, it would typically have to be unique, and a logo should be incorporated
It would be hard to know,
however if you store is successful, and others are trying to copy your store and use your store name and saying, you could then sue them
You would have to hire an investigator,
you can also go to the USPTO website to file a trademark for your logo or unique and special saying
You can look online in NY several investigators can do this,
you can also do a google search and NYS Corp search to see if your name is taken
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