Apparently, she was named after May an aunt of hers.
May Gamgee was born in TA 2976 (SR 1376) and was the fourth child and the second daughter of Hamfast Gamgee and Bell Goodchild of Bagshot Row in Hobbiton. Her youngest brother was Samwise Gamgee. She has three older siblings Hamson, Halfred and Daisy. Her other younger sibling is Marigold.
Nothing further is known about her life or who she married (if she did) or when she died.