Transferred use of the Scottish surname, in origin a local name from a minor place on the River Tweed, named as ‘the stream (Old English well(a)) of Mack’. The latter is a form of Magnus. Maxwell was the middle name of the newspaper tycoon William Maxwell Aitken, Lord Beaverbrook (1879–1964), who was born in Canada, and it has been used as a given name among his descendants. It is now also frequently taken as an expansion of Max.
English: from Middle English more ‘moor’, ‘marsh’, ‘fen’, ‘area of uncultivated land’ (Old English mōr), hence a topographic name for someone who lived in such a place or a habitational name from any of the various places named with this word, as for example Moore in Cheshire or More in Shropshire.