Can someone tell me what kind of fish this is ?

Yup, female blue star leopard wrasse. Great fish for an established tank as they feed a lot on copepods. Once they settle in they'll eat most offerings but sometimes that takes a while so a good healthy stock of pods and live foods, if available, go a long way.
 
I have a pair. They were responsible for absolutely decimating my flatworm population, including carefully plucking each and every one off of my LPS, especially in rather large Elegance that seemed to be a FW magnet.

Two of my very favorite fish, and certainly the hardest workers in the system.
 
I've often wondered how one of these would do in my system with a mandarin. Probably not good would be my first guess.
 
They sleep buried in the sand, so at a minimum, you'll have to provide a plastic bowl with 3+ inches of fine sand. I got mine about a month apart, and they both did fine in QT (more an observation tank - after 2 weeks or so and a round of Prazipro I put them in the DT, where LW #1 started swimming around hunting right off the bat. LW #2 buried itself in the sand for about a month - I had given it up for lost - and then one day appeared out and about, hunting with her? buddy. They are always together now swimming amongst the rocks, on the hunt for something tasty.
 
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