Last name help.

Hi there I recently found out I am part Jewish and I did some digging and found out My grandmothers maiden name was Shaw, which after googling the name seems to be either Scottish, English or and English version of a hebrew name. Although my grandmother was from England she would have been mostly Ashkenazi jewish with some middle eastern so it wouldn’t make sense for the name to be of Scottish or English origin. So FINALLY to my question, would anyone happen to know which jewish last name it would come from? I’ve found a similar Ashkenazi last name ‘Schach’ but I don’t know 100%. Any help is appreciated.