Companions can help you out in battle, which aids in not needing to feed as many mouths, and can offer some trinkets/pebbles as you play with them.
As far as pairing them with wolves, some pairings are better, but it's not important unless you really want to make sure you're getting the hunts. They can all be shuffled around as needed, so it's more get a setting that you like.
Companions are creatures that help your wolf in Campaign and also give you free stuff when you click/tap the button that says 'play'. In order to find that button, you have to go to the wolf who has the companion's profile. You don't really need to care about pairing them unless you're doing the Hunting profession, and if you are, look at the Synergies. I find that it's useful to pair a Kit with a Rodill for certain hunting quests.
Some other companion advice would be to give a stamina-giving companion (like a rodill or a folium) on your mining wolf and your fishing wolf, so that whenever you play with your companions you can fill up your stamina bars to keep going without spending food points there.
If you need pebbles, putting kapuras or furlog deer onto wolves are the cheapest way, since those only cost 450 pebbles from the mole market, are commonly in the mole market, and pay for themselves quickly.
If you wish to level up your wolves quicker, putting XP-giving companions like basidio toads and kuzma will significantly assist in that. Basidios are the cheapest at 450p each.
Just one last note; keep in mind that you are not able to switch them around as long as they are still on their playing cooldown. Which is okay-ish (I'm lying, I mean hella annoying) for those with a relatively short cooldown (1 hour), but is a nightmare for those with longer cooldowns.
