I know that when I go to add a sticker to someone's collection I'd like to see if they already have it since I like adding stickers they don't have to their collection. I know I can scroll up and down and look but when there's hundreds of stickers I can easily miss it. If the names were listed under the stickers I could easily use the CTRL+F function.

I'd like to see this, but only if the sticker albums could be paginated. Having all these items and their names all on one page would make the albums look messier than what they already are.

If this can't happen, maybe a search-box similar to the one on the achievements page would be a good alternative to what the OP suggested.

I'd like it if stickers could be organized and actually stay where you put them.

That said, maybe have a view option where you only see a list of names & don't have to wait for all the graphics to load. Maybe a "search a friends sticker collection" button or menu option somewhere?