Honestly, as @the8thark has already pointed out, there's only one alternate ending, which isn't crazy uncommon for Zelda games. Spirit Tracks had 3 different endings, but it didn't divulge into three separate timeline splits or anything. The likely answer for what will happen is there will be a...
http://nintendowire.com/blog/2017/01/20/legend-zelda-breath-wild-multiple-endings/
I'm guessing they'll just be based on how much memory you uncover, and less based on the choices you make in the game story-wise.