Yes Jerome "Jerry" Leiber used his wifes name, but it is the work of Wheeler and Leiber...
I sing this song and I'm sure that it's Japan, pronounced Jay-pan, accent on the Jay. It makes sense in the sense that both Johnny and June had a great sense of humor and utilized it frequently in their act. I understand as a performer the value of intelligently poking fun at yourself and I don't think there is anything strange about the way they recorded this song.