The name of Nye as a family name made its first appearance about the middle of the thirteenth century in the Sjelland Section of Denmark. At that time there were great internal uprisings in Sweden and many of the Swedes fled to adjoining countries to escape the dangers which threatened them at home. These people settled in little communities throughout Denmark and we find traces of their settlements in such compound names as Ny-borg, Ny-stead, and other towns named after their Swedish homes; in like manner to the naming of New Amsterdam by the Dutch settlers in America; the prefix Ny is the Danish language, meaning new or new comer.
In the adoption of surnames which hitherto had be practically unknown they employed much the same method, much the same method. Great confusion often resulted from the lack of a surname and so to distinguish a man he was given a surname which suggested itself some characteristic of the man, as for instance a trade or occupation, such as Baker, Carpenter, or Gardener, often his figure made the necessary suggestion, as Broad, Short or Tallman; or the simple addition of son as Johnson, Williamson or Robinson.
"The Danish family of Nye bore as armory, azure, a crescent in-crescent argent; crest, two horns couped, counter charged azure and crescent. None of the family ever took the trouble to have this confirmed in England, and no original grant of the Nye coat of arms appears in English records." A Genealogy of the Nye Family, Vol II, pg. 12.
And so one of these emigrants from Sweden was given by the inhabitants of his new country the name Nye or Newcomer.
For the ancestry of this man we must look to the traditional history of Denmark. there are several stories of his origin but one will be sufficient to give us a point from which we may start. this traditions tells us that about the middle of the thirteenth century a person came and settled in Fredericksborg, Bailiwick and Slangerup Parich in the Sjelland Section of Denmark. there was a rumor that the was the descendant of Harold Blautand who died in 985, through his daughter, who married one of the most famous of the Swedish heroes, Stryibiorn, son of Olaf, King of Sweden.
Lave Nye was a son of this descendant of the royal house of Sweden and is the first whose name appears on record. He became a man of great prominence and in 1316 was Bishop of Roskilde in the Sjelland Section (Lexicon over Adelige Familier in Denmark, Norge og Hertogdommene).
Source: Nye Family of America Assoc. 1903-1963 60th Anniversary of the First Reunion, pg. 6.
You can learn more about the Nye family in America at [http://www.nyefamily.org which is the Nye Family of America Assoc.
See full text of "A Genealogy of the Nye Family" Vol. IV at [http://www.archive.org/stream/genealogyofnyefa03nyeg/genealogyofnyefa03nyeg_djvu.txt
Nye Family of Burlington, VT: [ http://moorsfieldpress.com/genealogy=nye_mayflower_A_011-web.html]