A druid has cast awaken animal on her animal companion.
Per the rules, an awakened animal cannot also serve as an animal companion. If an animal companion becomes awakened, it ... ceases to be an animal companion, which means it reverts to a normal version of that animal. ...
You then add the 3d6 Intelligence, +1d3 Charisma, and +2 HD to the now-normal animal. At that point, the animal becomes a magical beast (augmented animal) and can begin gaining class levels as a monster cohort per the Bestiary rules...
Let's imagine that a druid did such a thing, and shortly thereafter perished.
What type of animal would you think most likely to be making a name for itself in the world?
One of a social species that doesn't look too scary, I'd guess. Antropomorphic Meercats or Tapirs or some-such should be fine.
Are you asking, what animal would WANT to make a name for itself or what animal would FIT IN to normal (whatever that means in your campaign) society? I am going to comment on the basic list, you can apply the logic to the full list if you want to.
One that is typically domesticated, dog, hawk or horse/pony/camel would get along nicely. Ones that are wild/threatening might find it harder to fit in to humanoid society. An ape would be interesting, with maybe a way to hide/disguise themselves as a typical humanoid.
IMHO, any that are social would want to make a name in society. Wolf, horse/pony, dog or ape seem to be fairly social. I don't know enough about some of the choices to know. Are camels herd animals?