Why would Rhaegar knight the Mountain? Even ignoring Gregor’s reputation, is House Clegane really important enough to warrant the Crown Prince of Westeros’ personal attention?

We don’t know the precise circumstances of Gregor’s knighting, but two possibilities come into mind: either it was done as a favor to Tywin Lannister, as Gregor was his bannermen, or it happened as a result of Gregor’s prowess during a tourney or melee, which is pretty common.