Please forgive a newcomer to this forum, but I must disagree with Norm about the origins of the Ashton name.
The first to be known by the name was Orm fitz Roger, also known as Orn de Ashton, second son of Roger fitz Orm, Lord of the manors of Ashton, Kirkby-Ireleth and Heaton-in-Lonsdale. Orm was granted Ashton under Lyne by his brother, William fitz Roger, who kept Kirkby Ireleth and Heaton-in-Lonsdale. Roger fitz Orm's father was Orm fitz Ailward, son of Ailward, Lord of Ormskirk, living 1133, son of Dunnic, son of Orm fitz Magnus, Son of Magnus, Thane of Halton in Cheshire at the time of Edward the Confessor. Of mixed Norse and Saxon descent, he was killed by the Welsh.
The main branch died out as lords of the manor soon after 1515, when John Ashton, son of Sir Thomas, died childless.