Amy's entry:

I have been driving through the state of FL all day long with the girls, but the car trip gave me the perfect name, one that would help your sheep make a grand impression at any gathering. Because every sheep needs to make a good impression.

You could call her Cy Lynn. (Cy is a nickname for lots of Greek names, including Cybele, an ancient nature goddess.) This way, you could introduce her formally in your best dramatic voice:

I'd like you to meet Cy Lynn...Of The Lambs.

(for your unwanted guests, you could always follow this up in your best creepy voice: Are the lambs still screaming, Clarice?)