After thinking this over, I'm not sure if calling it the "Joey" is a good idea, I guess it depends how savvy your groomer is, and if she's heard about the world famous Joey.
Here's a couple of other popular Joey's:
This cut may not look too bad on a yorkie, however,

if the groomer has this in mind, you might be a little disappointed.
Unless your groomer is world class, you might just want to call it, Modified Schnauzer with a puppy head.