The Ensinge family is found in the records of southern England back into the 1300s, when they were recorded with the name "de Ensyng". I haven't yet found time, but soon intend, to check the Domesday book to see if Ensyng is a place.
In 1918, Charles Sidney Ensign Jr.(2) suggested that the name derives from a place called Ens, "a small fishing village on the isle of Schokland in the Zuyder Zee, included in the region then known as Frisia and now a part of the Kingdom of the Netherlands."
Martha Eunice Ensign Nelson, in her genealogy of immigrant James Ensign(3), writing of the historical background of the Ensign family, mentions Sir Robert Ensign, who owned lands in the neighborhood of Chilham, in Kent, in the year 30 Henry VIII (1538).
The IGI contains extraction from the parish registers of St. Stephen, Norwich, Norfolk, baptisms of four children of a John Ensinge between 1591 and 1599, and a marriage of Anne Ensinge there in 1617.
Somehow the English name "Ensing(e)" came to be transformed into the American name "Ensign." My theory is that standardized spelling was becoming more widespread in those days, and the population was growing, and thus clerks familiar with the standard came more often in contact with members of the public not known to them. It's probably to the advance of bureaucracy that the American family owes its name.