There's two commonly used spellings for the name of Gerda's friend in "The Snow Queen": Kay or Kai. We are going with
the spelling utilized by the Hans Christian Andersen Center, which specializes in Andersen research. It's also the spelling in the book of Andersen fairy tales I inherited from my mother when I was a little girl:
This book is 51 years old and belonged to my mom when she was a child. Aren't the illustrations gorgeous?