I'm mystified by this fish of yours...so much so I decided to break out my fairy wrasse book to see if yours appears...and sure enough, it does.
It's also called a "Schwartz's Wrasse", commonly found in Bali and near SAnta Cruz Islands...it is a relatively small wrasse (max size about 12cm--so yours is probably full grown) , lives in shallow sea beds, or lagoons at a max of 2 meters...likes open sand beds, rather than reef structures...they WILL eat your inverts (most wrasses will)...so small crustaceans are probably toast.
Males are identified by their cheek patterns and unusual dorsal fin shape.
They also are said to do very well in home aquariums, and can live many years in captivity.
In larger aquariums, more than one member of the genus can be kept together.
Source: "Fairy and Rainbow Wrasses and Their Relatives" by Rudie H. Kuiter (good book on wrasses, but difficult to find--at least it used to be...
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Have fun with that fish, he's a beauty!