Music wise, that is a new track that is not yet available out of the game (or even on the Orchestrion in game sadly), so it's actual track title won't be officially known until the Stormblood OST album is officially released (when that will be is anyone's guess).

As for the falcon as a mount, players do get a white version as a personal mount during SB's main scenario, so keep playing (although alas it merely plays Borderless, the default HW flying mount theme instead of that new theme the falcons have sadly).