I have heard them called "Borkies" my some breeders. Occasionally the breeder will use the name of the larger animal first. In most breeding scenarios, this would be the Bichon.
A Yorkie-Bichon mix dog, is a cross between a Yorkshire Terrier and the Bichon Frise. This mixed breed dog is usually called a YoChon, or Yo-Chon. But some people refer to it as Bichon Yorkie.