i think it would be better if only the exact name you inputted on the search box will appear, for example, you are going to search for a RainbowMew, RainbowMewtwo will also appear and it is kinda annoying,

another idea is that there is a separate box where you can choose the type/color of the pokemon(cursed;shadow,etc.) and the another box where you can type the name of the pokemon, that's all.

Hmm, i think its there..! Check the box next to a blank box where you can type. Maybe it shows a particular type of poke. If it's not, your idea is awesome. I'll give 10/10 for it