Many of the "Door's" found in Maine and New Hampshire may very well be descended from Richard Door of Portsmouth, NH. Before the early 1800's it was commonly spelled Door in the early sources - sometime after 1800 more common spelling changed to Dore, Doar, Dorr, or Doore; few families in the Maine/New Hampshire area kept Door.
My own GGG grandfather Joel Door was married (to Hannah Hussey) in Shapleigh, ME in 1800 as Door, moved north to Harmony, ME where the town record used Doore for all the related families until after 1820 when they changed to Dore (with a change of the town clerk shown by a change of handwriting).
GGG grandfather Joel moved away to Dover-Foxcroft from Harmony in 1811, and kept Doore, however some of his children changed to Dorr in the mid 1800's. The early handritten records of Piscataquis County use Door, Dore, Doore, Doar, and Dorr in records of our family, sometimes more than one spelling on the same page.
So there we are; Door, Doore, Dore, and Dorr - all cousins.