If you are getting a group lesson, you typically can not request a specific instructor. You simply show up at the resort, buy a lesson, show up at the right time and rely on the resort reputation that will give you a qualified pro.
If you are getting a private lesson you can request a specific instructor. The Epic instructor listing only has one pro for New Hamshire (Bob Hatcher at Waterville Valley). That's one source for recommendations. Eventually, someone here on Epic is likely to give you a specific recommendation for one of the resorts you listed. In the absence of a specific recommendation, you can request an instructor with PSIA Level 3 certification or equivalent and have a very good chance of finding a good instructor.