I think of
May as a month and
Mae as a name. Also, my great-grandmother's MN was
Mae and my sister's after her.
I wouldn't assume the spelling, but ask straightaway.
I know many people with
May or
Mae as a MN. Upwards of 10. I also know an
Anna MaeRose who goes by
Mae.
The more common it is as a MN, the more I want to see it as a FN!
I think
Mae is very attractive and I would consider using it (possibly as a nickname for
Mary).
Maisie sounds too flimsy for my taste.