What about Timmy?
quick story: we rescued a kitten on christmas day. 4 months old, absolutely tiny, big ball of fluff. We thought she was a boy but it turns out she was a girl (obv. by the pronouns). We named her after Tiny Tim and that is how my baby girl (now 8 years old) got her name.
Here she is asleep on my desk:
Failing that, I think Jingle or Kringle would be adorable.