https://www.youtube.com/watch?v=U85yH-1P7tY 15 min Wolf Link Guide.
I learned halfway thru my game a long time ago that the closest you can get to having a 'dog' as your man's best friend is using Wolf Link Amiibo which BOTW supports on both Wii U and Switch. What it does is Wolf Link will be 'summoned' from the 'otherworld' and not only join you but even fight for you along side your adventures. HOWEVER unless you own TPHD for the Wii U your stuck with only 3 hearts for Wolf. Meaning he can die pretty fast and is practically useless.
CEMU users these restrictions do NOT apply:
Somehow INSIDE THE NINTENDO SWITCH there is an internal checksum to detect not only ownership of TPHD for the Wii U but it goes as far as detecting if you did the cave trial thingy which once you 100% it your Wolf Link has it's hearts all maxed out carried over to both BOTW editions.
I find that pretty bizarre Nintendo choose to do that but at least it doesn't cripple the game if you don't have the accessory unlike (cough) Skyward Sword) cough) Amiibo.