From Wikipedia (https://en.wikipedia.org/wiki/David_Thompson_(New_Hampshire_settler)):
"David Thompson or David Thomson (1588 - disappeared 1628) was an early Scot settler of the New England area, considered the founder and first non-native settler of New Hampshire. He was granted a land patent for Thompson Island in Boston Harbor, which continues to bear his name. According to Burke's Landed Gentry (2010), his family—the Thomsons of Corstorphine—are direct descendants of a great-grandson of King Robert II of Scotland, namely, Sir Thomas Stewart, Master of Mar."
It seems fairly certain that David Thomson was the first non-native settler of what is now New Hampshire. The colony that became the state was founded on the division in 1629 of a land grant given in 1622 by the Council for New England to Captain John Mason (former governor of Newfoundland) and Sir Ferdinando Gorges (who founded Maine). The colony was named "New Hampshire" by Mason after the English county of Hampshire, one of the first Saxon shires. John Mason sent David Thomson to set up the first settlement.
David Thomson first settled at Odiorne's Point in Rye (near Portsmouth) with a group of fishermen from England in 1623, just three years after the Pilgrims landed at Plymouth. The settlers built a fort, manor house and other buildings, some for fish processing, on Flake Hill at the mouth of the Piscataqua River, naming the settlement "Pannaway Plantation".
Several years later, David Thomson moved his family to an island he acquired as part of his compensation from the Council for New England in what is now known as Boston Harbor in 1626. They became the first European settlers of what would become Boston, Massachusetts in 1630.
David disappeared in 1628 and was never heard from again. Some historians theorize he was the victim of foul play, as he was at times called upon to serve as mediator in hostile conflicts and negotiations between expanding English groups and native inhabitants. Others suggest that he accidentally drowned in the harbor.