These cute creatures are called Dynamons.
As you progress through the game, you will encounter plenty of them.
The game begins in a place called Camp Dynamon.

Dynamon
You will get one Dynamon for free from the camp.
There are three Dynamons to choose from: Snorky, Torchip, or Kikflick.
There are many other Dynamons, and you wont wait too long to meet them.

Each Dynamon has unique fighting abilities, but they have one similarity.
All of them are cute.
you could also upgrade the Dynamons to increase their power.

Items
There are some items in the game that can help you to fulfill your mission.
Fire Dynastone and Earth Dynastone, for example, are the items to level up some Dynamons.
Discatch is the item that you will need to collect more Dynamons.

Some items are useful to help you win battles.
Snorky is a dynamon that looks like a small elephant.
Some of its skills are Sonic Shock, Bubble Burst, Flash, and Frozen Mist.

Also, once the creature reaches level 10, another powerfull skill named Iceberg is unlocked.
Torchip can evolve into Scorchite, for example.
The evolved form looks different from the original one, but it still looks adorable.

Even though their appearances change, they still use the same elemental power.