How does the dorsal fin look when it flash? Semi-pointy? Can't really tell by the color of the photo. May be its a type of Flasher Wrasses. I have a wrasse that is similar to yours and the upper portion is more of an dark/wish off red color. Over time the tail fins and part of the belly will turn into a rich dark purple when the fish is excited.
looks more like a fairy than a flasher. grisha why you worrying? you can put that thin in the tank. they are fairly peaceful, i don't see why it will fight w/ your goby.
I'd say definitely a fairy wrasse and not a flasher, and it does look odd species wise. Either a female or a juvi. in transition would be my guess. I see no problem with adding him to your display. If you remain reluctant, I'll take him off your hands. Randy