Based off shape and what I can see of the eye I would guess that is some sort of fairy wrasse. I would make sure u find out details on any future wrasses you get. Many sold in the hobby get quite large if you have a smaller tank....and even in a larger tank the larger ones often will decimate your cleanup crew(like a checkerboard, banana, melanarus, etc). Others like a red Coris wrasse are stunning and one of my favorite wrasses but will knock everything they possibly can over. At full size this can include even decent size rocks. Even in their juvenile phase have had them turn over 12 inch wall hammers completely upside down.
What wrasses can go together largely depend on size and character(rockwork,etc) as well as individual fish personalities. I am sure people with more wrasse knowledge may have better suggestions. I generally try to avoid ones with similar body shape or colors.
In a 115g shallow vat tank for example I have 3 yellow Coris, a sixline, a bluestreak cleaner, a blue throat fairy wrasse, and a red Coris wrasse. Probably not recommended, but has worked out much better than expected and no aggression issues at all, but it's a big footprint(I think around 68x30 or something like that) and a lot of places for them to have their own spot(though the three yellow Coris all hang out with each other).