I know the setting of the game takes place 20 years after the battle of Five Armies, if I am not mistaken. And future supplements will take us upto the War of the Ring.

During the Fellowship, Grimbeorn the Old, son of Beorn and Brand, grandson of Bard are in charge of the respective factions.

I'm curois, since Beorn is such a mysterious character around when in the timeline, if it is even known, when Grimbeorn becomes known? Or is the first mention in the Fellowship?

It's 5 years afterwards, actually.

I honestly can't remember whether there is any mention of Grimbeorn apart from in the FOTR. However, I have been thinking about the suggested campaign in the Loremaster book about the darkening of Mirkwood and the apparent lack of part played by the Woodmen in the war of the ring.
This is what I came up with. Grimbeorn is the child of Beorn born of a Woodman mother. Having finally found a leader that can unite them, the Woodmen and the Beornings have, more or less, assimilated into one people in a possible tribal confederation.
Not all the Woodmen have joined Grimbeorns tribal confederation though. Many travelled to the newly rebirthed kingdom of Dale. The last paragraphs of 'the Hobbit' state that men came from the south(Long Lake and the settlements of the River Running) and the 'west'? Unless we count the potential for unmentioned settlements of Northman stock in Arnor/Eriador, these westerners can only be Beornings or Woodmen IMO.
The disappearance of Radagast remains a mystery though........

5 years correct! Thank you kindly for the information.