My idea; litnya, lutnya ....
Because in my (Slovenian) language 'lutnja' is a name for an old instrument from middle age (Persia). The name lutnja itself means wooden instrument, it has curved shape and strings also, just as ukulele. You can think something out of LUTNJA, but I don't know how do you want the name to sound, or more exotic or english... I can come up with more ideas, if you let me know.
Anything else that you need?
I can also design the typography and logo for it if you like.