Public Official Registered A Competitor's Business Name During A Filing Gap And Put Up Fake "store Closing" Signs—what Are The Civil Remedies?

Location: Milton NH

A local family-owned home business in New Hampshire (Pat's Prims) has operated since roughly 2015. While the business was recently refiling state LLC paperwork to correct a date error, a sitting town official registered a nearly identical name (Pat's Prims Country Store and Farmhouse Decor) under his own name with the Secretary of State.

Since registering the name, the official has engaged in the following actions:
Misleading Signage & Business Interference: Placed commercial signs just off the business's property line falsely claiming the store is closing and asserting he is the owner.
Targeted Harassment: Parked at the property line honking his horn, driven by the family's home uninvited, and watched the signs from afar (there is an active no-trespassing ordinance against him).
State Registration Status: Secretary of State records show two separate active registrations: the family's original business name and the official's newly registered DBA/LLC name registered to a different address.

While code enforcement and ethics reviews have been requested through the town's Board of Selectmen, the business owners are seeking guidance on private legal remedies.
Questions:
1. What civil causes of action exist for tortious interference with contractual/business relations, common law trademark infringement, or unfair competition/trademark squatting in NH?
2. Does registering a slightly altered DBA/LLC name give a party any legal right to claim ownership over an established existing business or appropriate its goodwill?
3. What is the fastest court remedy (e.g., Cease & Desist, preliminary injunction, or restraining order) to compel the removal of deceptive signs and stop the harassment?