Although beautiful and distinctive, this soldier fly (Hedriodiscus trivittatus) does not have a common name. All members of the entire family to which it belongs, stratiomyidae, are called soldier flies. Many of them are bee or wasp mimics, but they are harmless and do not sting or bite. I've sometimes heard people insist that they've been bitten by this fly, but they are probably confusing it with deer flies, which can also be colorful with patterned eyes and live in similar shoreline habitats.
This particular species is about 1/3 of an inch long and, while not very common, is usually seen feeding at flowers, where it's gorgeous plastic-green color draws attention. The larvae are aquatic, look sort of leathery and elongated, and live at the edge of muddy, swampy or stagnant ponds.