Common names can be anything we want and there are many color, shape and size variations within species. (Homo sapiens for example.) Since most of us cannot scientifically ID fish, we can call them whatever feels good. A google search for seagrass wrasse turned up mostly images of what is also called a Dragon Wrasse, not the same as what you have. The Common Christmas Wrasse is also not what you have there, but that's as good a name as any, since it's red and green.

I'd check out Fairy Wrasses to see if there is a match.