From the name of a river in Ireland. It is not clear why it has become so popular as a given name; compare Clodagh. In part it may also be a transferred use of the Irish surname, Gaelic Ó Seanáin ‘descendant of Seanán’ (a diminutive of Seán). Shannon is not found as a traditional given name in Ireland itself.
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.