As a medieval given name this is a Norman form of the French name Thierry, from Germanic Theodoric, from þeud ‘people, race’ + rīc ‘power, ruler’. This was adopted by the Normans and introduced by them to Britain. In modern English use it seems at first to have been a transferred use of the surname derived from the medieval given name, and later to have been taken as a pet form of Terence.
English (especially Yorkshire) and Scottish: occupational name for a fuller, Middle English walkere, Old English wealcere, an agent derivative of wealcan ‘to walk, tread’. This was the regular term for the occupation during the Middle Ages in western and northern England. Compare Fuller and Tucker. As a Scottish surname it has also been used as a translation of Gaelic Mac an Fhucadair ‘son of the fuller’.