It was a home for gargoyles since time immemorial, and also had a series of human strongholds built upon it, whose builders and occupants formed a series of (temporary) alliances with the local gargoyle clan. The present-day Castle Wyvern, built in 971 and sacked in 994, was the last such stronghold. ("Awakening: Part One") 
Goliath, Elisa, Angela, and Bronx visited Wyvern Hill during the Avalon World Tour. In 1996, Wolf encountered Hakon's ghost at Wyvern, and left a motorist stranded in the process. ("Shadows of the Past", "Vendettas")
At some point between 1996 and 2188, gargoyles (possibly descended from the original Wyvern Clan - most likely via the Avalon Clan, Labyrinth Clan, and Manhattan Clan) will resettle here and found a new clan at this place. They will also be known as the Wyvern Clan. 
The hill may have been named because of the resident gargoyles; in medieval legend, a wyvern is a two-legged dragon, and it is quite possible that superstitious Scotsmen may have found it easy to confound gargoyles with dragons or wyverns. When directly asked if there was a reason the hill was named after a dragon species, Greg Weisman replied, "if you come to a Gathering, you'll get a clear hint of what that is when you see the DARK AGES pitch". Although the pitch does show the alliance between humans and the local clan, it also includes an image of gargoyles fighting a dragon.  The Archmage is also seen scheming with his ally Iago, who is known to use the phrase "by the dragon".