Ailsa

Ailsa Craig is a volcanic plug in the Firth of Clyde in Scotland. It is partly comprised of granite that is used for curling stones. The granite is the hardest and most durable to be found anywhere in the world.
I was a personal friend of the late Lord Charles Kennedy, Clan Chief and Marquis of Ailsa. I once asked him what Ailsa meant but he body swerved it. I am sure that he was well aware that he was The Marquis of Fairy, this being one of the translations of the original Viking word. My only grandchild is an Ailsa.

'Modern Scottish name from Ailsa Craig, a rocky islet in the Clyde estuary off Ayrshire coast. Derived from Old Norse-Viking Alfisigesy "island off Alfsigr"; composed of alf "supernatural being, elf" + sigi "victory". Possible anglicization of Ealasaid. Ailsa Craig is known in Gaelic as Allasa, or Creag Ealasaid. Form of Elsa from Hebrew Elizabeth, "consecrated to God."'
Source: http://www.amethyst-night.com/names/scotfem.html

I've also read that Ailsa Craig's origin is Gaelic Aillse Creag, which means "fairy island".

The meaning you have I don't think is right. I am called Ailsa and I think it means fairy, and it can mean rock, so it means fairy rock.