Sharing and profile

Your in-game nickname (Settings) is your public name in RepDex. Use your Pokémon GO trainer name so trading partners recognise you.
Your collection itself is private. Only the wishlists you switch to Show in public are shared.
Your public page is /user/<nickname>; the link is at the top of your Wishlists page. Add #shiny, #xxs and so on to link to one list.
Or send a picture: Save as image on a wishlist.