Is there a word for the towel on a waiter's arm?

"Napkin" or "towel" seem so...ordinary. Is there a better word for it?

Napkin is the correct term:

• what about that waiter who carries a napkin draped over one arm? In part, it’s practicality. It’s readily available to mop up any accidental spills or other messes at your table. But the practice dates back a couple of hundred years in France; that was how waiters carried the napkins they would distribute to diners. Napkins have been in use for thousands of years.

If you want a less common alternative you can use serviette:

• (chiefly British) : a table napkin

You might want to use the French word for that napkin. In French it's called liteau. The plural should be liteaux.

In the F&B industry it is termed as "Waiter's cloth".