Hugh's by-name 'Emme' or 'Heem' is derived from the OE word eam, ME eme, meaning 'uncle'.
The modern surname forms are Eames and Heams.
The most likely explanation was that Hugh's by-name referred to his great-great uncle, Humphrey de Berkeley (Barclay), who was certainly much more powerful and famous than Hugh, whose descent from Humphrey is based on his matronymic Constance, and may have involved an illegitimate family member. Perhaps it originated as a nickname due to repeated reference to his famous 'uncle'.
The use of the Middle English term is also interesting here in terms of the use of English speech in Angus rather than French or Gaelic in the late thirteenth century.