What is this "Order of the Trout?"
Well the trout is the insignia of the Tully family, Liege Lords over the Riverlands, one of the 7 Kingdoms of Westeros. But the Tully flag is a fish on a field of red and blue, and I see nor red nor blue in the Order of the Trout medal.
However, there is Bryndyn Tully, seasoned war vet and Uncle to the Heir of the Tully family. Bryndyn has taken on the moniker "Black Fish," and uses it for his personal coat of arms. In Westeros the BLackfish has historically been known for his experience in combat and for his desire to go against the curve, or "swim upstream" as some would call it.
But what does the BlackFish have to do with The Order of the Trout in Illyriad????
In Westeros, the Blackfish's whereabouts remain unknown. He was last seen mysteriously disapearing from a surrounded and sieged castle after his own family yielded the castle to the enemy. The common folk believe he has gone to rally what is left of the Young Wolf's forces to oppose the Tyrinacal Lannister control of the Riverlands.
Clearly the Order of the Trout is formed and named as a node to Sir Bryndyn Tully, The Black Fish. This is inline with the much publicized Order of the Phoenix, named after their idol Albus Percival Wulfric Brian Dumbledore. Since they are named after the Black Fish, they wish to represent is "swimming upstream" mentality. Furthermore it shows a unified force existing through many lands of Elgea.
Now that we know where the name comes from, we can theorize as to the purpose of the Order. I believe they are mimicking the Blackfish. They are forming a coalition against the current tyrant in the largest war plaguing the future of Elgea. The Order of the Trout will continue to rally forces and rise up against the oppressors to bring balance and prosperity to the realm.