(こちらは) 私のともだちのクリステイです
(this is) my friend, Christy.
This presumes that her friend is standing next to her or something getting introduced. BTW if it's pronounced like Agatha Christie it would be クリスティ, small i.
[MENTION=60792]shenrais[/MENTION] Your sentence is not grammatically wrong, but it's not a way to introduce someone to another person. It's fine if you are describing your friend to someone when she's not there. "My friend's name is Christy."