Emerald is May's birthstone. There were 124 baby girls named Emerald in 2011, which jumped up to 193 girls given the name in 2015, now ranking just below the top 1000 at #1357. Esmeralda, which means "emerald," has been much more popular, with 942 births in 2011, while Emeraude, the French version, has seen no love. Jade, another green gemstone, is also very popular, with 2,655 births in 2011. Both Esmeralda and Jade ranked in the top 1000, along with Ruby, Pearl and Diamond. An obvious nickname for Emerald is Emmy.
Emerald is the green variant of Beryl, which was a popular name decades ago and is now considered vintage. Emerald was considered the stone of the goddess Venus, which just so happens to be the ruling planet of May's astrological sign: Taurus, the bull. It was also thought to be the fourth foundation in the Kingdom of Heaven in Revelations. (FYI, another great May name is Tauria.)