You first learn about the dog in the "New kinds of ally" quest (and learn his name is Pouch). After this quest, you must become friends with Sylvie Dawson (by earning 250 points with her). This can be done by, once a day, finding her dog in various zones and completing their task. Each task will earn you 25 points, thus requiring at least 10 days to complete.
After getting 250 points, return to Sacramento Suburbs and talk to Sylvie Dawson. A new quest will unlock. After this quest, you have to become friends with the dog (by earning 700 points).
RenownEditAfter befriending Sylvie Dawson, you can begin gaining renown with the dog to unlock it as a companion.