This idea is kinda for showing off your pets and will change depending on the caught pet.
I think the best way to explain my idea is through a example:

This is my pet Lobo who will be my demonstration.
Lobo I caught in the middle of a zombie invasion at the Sanctuary of Sarielle

My secret history idea is basically a back story of my pet to the point of when I caught so Lobo's would be something like this.
Lobo: Lobo was a wild and quite rare lupora who explored on her own and, one day while exploring she heard a groan and turned around and saw these undead elves coming out of the ground. She ran and, led these creatures to the Sanctuary of Sarielle to try to get away she then ran into Peace's net blindly why his pets fought the zombies attacking.
So this idea is to show off your pets by going like mine survived in the wild for 3 days without food or, mine fought bandits to the death on his own. This may make some of the captured pets a little more valuable if they actually did have a story of course there will be some normal captured pets which won't have a story making the secret history raise the value of the caught pets that do have them.
Of course this is only a idea.

That's a lot of customized detail per pet.
Imo, if a player really cared, they could make up a pet's background all on their own and post it on a profile pet page (I assume will come in the future, similar to neopets for example).

Realistically, if this were a thing, Krin would have to come up with some "history" that's duplicable across several events. I mean, if he wanted to be creative, he could come up with this, but there's SO many different events taking place, and WHAT are the chances that you're actually going to catch a pet, much less in a specific event?

Pets aren't generated until the time of their successful capture. Otherwise, what you see in the wild is just a randomized pet picture that you fight.

tl;dr this is something the player can plug him or herself. This can go hand in hand with pet profiles, customizable aby the player.

If that's the case whats the status on the pet profile customization? Have the administrators claimed that it's going to be made, cause now i'm curious?