Wrasses don't have 'mates.' Two fairy wrasses of the same species will not fair well together and in all likelihood will eventually become one.
From one of Evolved's threads...
About “Pairing” Wrasses, or Harems
In the wild, most genera of wrasses live in harems, which consists of a group of females to one dominant male. Often, there are a few transitional males in this group as well, which are essentially males-in-waiting – waiting for their chance to overtake the current or become the new dominant male. Within this harem, there is an established hierarchy; there are no bonded or mated relationships – it is all about the dominance of the terminal male and submission of the females and transitional males. This behavior is similar to that of anthias; wrasses do not “pair” like clown fish do.
In aquaria, it is rather difficult to successfully duplicate nature, in that all females tend to eventually transition to male, regardless of the presence of a more dominant male. Often, when this occurs in the presence of a dominant male, the new male may end up with best coloration. However, the survival of the old male is always questionable, and sometimes removal of one male becomes necessary for obvious aggression. For these reasons, I no longer bother with more than one specimen of a single species except in certain (rare) circumstances. I have attempted to keep a male/female pair/trio from the Cirrhilabrus, Halichoeres, and Paracheilinus genera, only to always result in all females turning to male with time.
Therefore, as an alternative to keeping pairs/trios/harems of wrasses in aquaria, an aquarist may wish to keep single specimens of each species mixed with others. So long as certain species are avoided, selections are made carefully, and in accords with the “About Mixing Species and Genera” section above, the results should be rewarding. Each specimen is highly likely to eventually transition to male, providing the best coloration. As an added bonus, the hierarchy of the group lends to displays of finnage and “flashing” of colors on frequent occasions for delightful viewing. However, the only catch with this approach is that some patience may be required. If specimens are purchased as juveniles or females, it may be a while before they transition into males. This time frame is widely variable, and depends not only on the fish’s age & maturity, but also the hierarchy established amongst the tank mates. In short, the timing is complicated, and may be as short as a few weeks to many, many months.
For more on “pairing”, see this article of mine (portions of the above are taken from here):
https://www.reef2reef.com/ams/pairing-wrasses-thats-not-how-any-of-this-works.3/
