Greeting Neath, and welcome to TORC, I hope you're enjoying it here.
No, sadly I haven't named any of my instruments after Tolkien characters or objects! My flute is called Freya but although it sounds like something potentially Tolkienesque, a bit mythological and Norse/dwarf related, I don't think she's mentioned by him! I did have a clarinet which I didn't name, and I haven't named my piano. Maybe I should name my piccolo after something or someone... Hmm...