Scottish and northern Irish: from Anglo-Norman French waleis ‘Welsh’ (from a Germanic cognate of Old English wealh ‘foreign’), hence an ethnic name for a Welsh speaker. In some cases this clearly denoted an incomer to Scotland from Wales or the Welsh Marches, but it may also have denoted a Welsh-speaking Scot: in western Scotland around Glasgow, the Welsh-speaking Strathclyde Britons survived well into the Middle Ages.
Jewish: this surname has been adopted in the 19th and 20th centuries as an Americanized form of various Ashkenazic Jewish surnames, e.g. Wallach.
Dictionary of American Family Names, Oxford University Press, Mar 2003