I believe that this question is asking about Bud's band name that he is given once the members of Calloway's band decide to care for Bud. This occurs in chapter 16, and the first suggested name is "Sleepy." That doesn't spark much support, so "The Bone" is suggested on account of Bud being really skinny. That name isn't universally liked either, so Mr. Jimmy tries to class it up by using "the French word" for bone (la bone). Steady Eddie then chimes in and says that they should mix the two suggested names, and he puts forth the name "Sleepy LaBone." Bud tells his readers that he couldn't contain his happiness with the name because he thinks it is the best name that he has ever heard.
I couldn't tie the smile down anymore, that was about the best name I'd ever heard in my life!
. . .
Sleepy LaBone. Shucks, that was the kind of name that was enough to make you forget folks had ever called you Buddy, or even Clarence. That was the kind of name that was enough to make you practice four hours every day, just so you could live up to it!