If the name is used on a good in interstate commerce or international commerce with the US, you could file for trademark registration. If it is not used, it cannot be registered, and names cannot be "locked up" without use Except with an Intent to Use mark. See www.uspto.gov to learn more about trademarks.
Generally speaking, the law of trademark protects this interest. But once you have abandoned the business, it will be difficult for you to assert trademark rights in the name. If you resume the use of the name, you can apply to protect it as a registered trademark. It may also be possible to protect it by filing an intent-to-use application. A trademark attorney can assist you in doing this.
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