From the experts:
May is a sweet old-fashioned name that hasn't been on the national charts in several decades, but is definitely sounding fresh and springlike. Parents are beginning to see it once more as one of the prettiest middle name options. May was as high on the list as Number 57 in the 1880s; it's now 228 on Nameberry.
May started as one of the innumerable pet forms of Mary and Margaret, as well as a springtime month name along with April and June. She's represented in literature by May Bartram in Henry James's The Beast in the Jungle and May Welland in Edith Wharton's The Age of Innocence.
Actresses Emily Morton and Madeline Stowe named their daughters May, and Eric Clapton and Jodie Sweetin used it in middle place for theirs.