I have been doing some research on the family with the surname of Edison/Ideson/Edeson/Ydesse/Eadeson and a bunch of other variations in New Jersey. In my family, I have some folks with the surname of Edison/Adson from Morris County, NJ. They seem to "originate" in the Second River or Belleville (Essex Co.) area and are found in the Second River Dutch Reformed Church records(early and mid 1700s). They lived at Acquackanonk (Passaic Co., I think) before and during the American Revolution. I do not know if there is any kinship with the John Edison, the Loyalist, who fled to Nova Scotia and then moved to Ontario. Among the Edisons living in the Second River area, the surname Edeson seems to be a corruption of the patronymic for son of Ide or Edo. Despite the propensity of the Dutch to have large families, there are not that many persons with this surname in notheastern NJ. I noted that there was a Cornelis Edeson in the 1800 New York City census. I have never invesitaged it but I certainly seems possible, if not probable, that some of the family crossed the river to New York City.
Also Cornelius or more commonly, Cornelis, is quite a popular name among the Second River family which clung tenaciously to the "Dutch" naming tradition. (First son named for paternal grandfather of the infant, second son named for maternal grandfather, etc.)
The patronymic Idens shows up quite a bit in the baptismal records of the New Amsterdam/New York Reformed Dutch Church records. Teunis Idens and presumably his sister Rebecca Idens seem to come from Kings County, NY. I do not know if there is any connection or not.