Underwood English and Scottish: topographic name for someone who lived near or in a wood, from Middle English under + wude, wode ‘wood’, or a habitational name from any of various places so named, for example in Derbyshire, Nottinghamshire, and the former county of Ayrshire (from Old English under + wudu).
Dictionary of American Family Names, Oxford University Press, ISBN 0-19-508137-4