What's the name of this dish (or name of fish) in these pictures?
Bouillabaisse is a traditional fish stew originating in the French port city of Marseille.  While the sauce in your recipe might have some ingredients in common with that dish, it is not a bouillabaisse.  Pictured is a firm, white fish.  I'm not sure I can identify the exact species, but it might be halibut or cod.  Given the sauce and the plating, I would say any firm, white fish would work in the recipe.