The occupational name of a person in the employ of an abbot - the rule of celibacy for members of the clergy implies that the name would not be as a result of clergypeople having descendants.
The term Abbott is Middle English, with its counterpart abbod from Old English, and abe(t) in Old French.
The Old English and French terms originate from Late Latin and the Greek abbas and abbatis words, meaning 'priest'. There is also a link to the Aramaic word aba which translates as 'father'. [1]