The Full Moon of May is known as Flower Moon to signify the flowers that bloom during this month. There is a myriad of wildflowers which bloom in May in the Northern Hemisphere, where these traditional Full Moon names originated.
For example, many types of anemone, wild garlic, indigo, bluebells, lupine, sundrops, and violets, to name just a few. It is no wonder that the colorful displays these flowers create in nature have inspired people to name this time after them.(https://www.timeanddate.com/astronomy/moon/flower.html)