English from the name of the tree [Salix spp], from Old English welig. The tree is "noted for its grace and the pliancy of its wood" [ONC]!

Note: ONC records only a female version of this name but a correspondent in Australia [CP] reports the recent use of Willow as a male name. The tree has no specific gender so we suppose it is as valid in this form as the female form!

See also Willoughby.