I'm reviewing "The Registers of Bruton, C. Somerset. Volume I. 1554-1680"
1587 July 2 Mary Walter d. of Nicolas Walter
1592 Feb 4 Mary Walter, d. of Richard Walter
I do wish the Christenings had listed parents as same name appear, in the same year. Keep in mind this was a register of many parishes. John, Richard, Thomas and Joan, Margaret, Mary also seem to repeat with Walter family records. EDIT: Records after 1586 does list the father.
While I have a PDF edition, if you search it seems to skip every 6th "Walter". So you need to manually scan. I'm working on a project to list every "Walter" mentioned to see if I can hope to assemble a family tree (Xpeor Walter is simple, but nephews have the same name).
Also keep an eye out for Waulter, Walters, Wallter, Watter, Watters.