There are state trademark laws, but usually lawyers prefer the federal Lanham Act to enforce trademark rights.
Here, however, the analysis might be more complicated than you think. Store names like "Big City Glass Corp" and like "Big City Glass and Mirror" are both probably too descriptive to even qualify as trademarks.
It takes an "arbitrary" and "fanciful" name, like "Apple" for computers, to make a good trademark. A suggestive one like "Microsoft" for computer software becomes strong over time as it develops "secondary meaning" in the minds of consumers, but a descriptive one like "Big City Glass" can never merit legal protection.
Maybe your ex-employees misappropriated some of your trade secrets, or are in violation of a non-compete contract, so you can go after them that way. See a lawyer for help.
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I agree with Attorney Koslyn. To answer your specific question; you can look at N.Y. GBS. LAW § 133 "Use of name or address with intent to deceive" as well as N.Y. GBS.LAW § 360-l : NY Code - Section 360-L "Injury to business reputation; dilution". Both provide for injunctive relief. Your best bet is to consult with a local IP attorney.
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There is no one statute that protects you in a situation like this---in fact, the main protection you have arises under Federal trademark law, not the state statutes cited by my colleague. You may have very legitimate trademark claims if you can establish that your business name acquired secondary meaning among consumers in your community, that the use of a similar name by your competitor is likely to cause consumer confusion. Note, however, that you may have a significant problem with regard to the specific example in your question------many courts would hold that the name "Big City Glass Corp" is descriptive and/or generic and, therefore, a very weak trademark. In order to prove your case, you would need to show that the name "Big City Glass Corp" acquired "secondary meaning" among consumers, who associate this name with your business (as opposed to other potential sources of the products you sell). Cases like this are very fact intensive, and merely citing a statute to your competitor will get you nowhere. You may have legitimate claims, here, but you can't pursue them reasonably without assistance of experience intellectual property/litigation counsel.