I photographed this little purple and yellow fish (3-4 inches = ca. 10 cm long) off the north coast of Roatan, Honduras last year. I was taking picture of something else, and this fish just got in front of the camera (hence a bit out of focus, the tail not in frame, etc.). I went through Reef Fish guide, several other guides, and some Internet sites with a comb, and yet I cannot place it.
It is mostly likely a species of wrasse or something closely related (Labridae) that I have never seen. The only other thing I can think of is Bluelip Parrotfish (Cryptotomus roseus), but I have never seen that one either. The interesting thing is that this fish possibly mimics a juvenile Spanish Hogfish.
I added another photo of the same species (and perhaps indeed of the same individual) that appeared on the background in another photo taken at same reef on the same date. It is out of focus, but the fish’s shape is clearly seen.
It has been suggested that this might be a juvenile Beaugregory. However, all damselfishes (including Beaugregory) are oval, with forked caudal fins, and their dorsal fins are continuous, rounded at the end, and extend to the base of tail. I added a picture of Beaugregory, although it is not a very good one.
In the fish in question the dorsal fin is also continuous, but it is narrow, not rounded, and it terminates well before the base of tail.
I found a picture of a similarly looking fish in DeLoach’s “Reef Fish Behaviour”, page 297. The picture suggests that it may be a female/initial phase of the Greenblotch Parrotfish (Sparisoma atomarium), although I would not rule out some intermediate phase of the Yellowhead Wrasse.