last name Udy says:
This interesting and unusual name is a variant form of the popular medieval English male personal name Hudd or Hudde, which has a complex origin. In most cases the origin is from the personal name "Hugh", introduced into England by the Normans after the Conquest of 1066. Hugh derives from a short form of various Germanic compound names beginning with the element "hug", meaning heart, mind, or spirit. The second possible origin is from an Olde English pre 7th century name, "Huda", as found in the place name Huddington, a village in Worcestershire. Finally, Hudde may have been used as a short, pet form of "Richard", another Germanic compound name introduced by the Normans and meaning "powerful brave". The variants of the modern surname Huddy, found as Udy and Udey, are frequently recorded in the West Country, more so than in London and the Home Counties. Examples are those of Digory Udey who married Loveday Coombe at Lostwithiel in Cornwall January 23rd 1785, whilst the first recorded spelling of the family name may be that of Richard Udie. This was dated 1544, when he married Alse Nanskevell, at St. Columb Major, Cornwall, during the reign of King Henry V111, known as "Bluff King Hal", 1509 - 1547. Surnames became necessary when governments introduced personal taxation. In England this was sometimes known as Poll Tax. Throughout the centuries, surnames in every country have continued to "develop" often leading to astonishing variants of the original spelling.

other sites also say originated in Cornwall, England and goes back to 1060 or so