Hi Lilred-
yep, I'm originally from NH but I left for college (and have been trying to get back home for the last 30 years!). Luckily I found a DE man who loves NH, and we'll move back in about 4 years or so. I still have family in southern NH.
I see others have already answered about the Lakes Region. It's very pretty, farther north than 'southern' NH, but not necessarily as remote/cold as 'northern'. It does get it's share of vacationers right around the lakes though. But it's still lovely area, and might suit you best.
As to being accepted.. yeah, NH folks take things slowly. They want to make sure you're going to stick around long enough for them to bother with (and not bug out screaming halfway through winter, or when you encounter hunting season with people bringing their deer home tied to the truck) and that you don't want to change things. If you take things slowly, are friendly and pitch in when help is needed, they'll warm up to you. NH folk in general make good friends: not false-friends, but real 'check on you in emergencies and lend a hand' type friends.
As to whether you'll ever be accepted as a local, or referred to by someone else's house.. it varies. A lot of people just don't have time to worry about that kind of thing. Sure my step mom is a navy kid originally from CA and my dad grew up in NJ. They moved to NH in the late 50s. I don't think anyone in town is at all concerned that they are 'from away'. We always refer to our previous houses by the name of the people who either built it (the Isaac Appleton House) or who we bought it from (the Chase Place), although sometimes those names change in town. The Chase Place for a while after the people we sold it to moved, was known as the Reilly house, and no one calls it that anymore. So... some old timers may use that as a point of reference, many don't. It may also depend on how old the house is. The Appleton house will always be the Appleton House no matter who lives there (the plaque on the door even says so) since it was built by an influential person. Other house... eh. but things can move slowly in NH. Just smile and don't let it bother you. In 20 years, you'll be doing it to.






