I believe both Monaco and Monte Carlo are towns in Monaco.

Monaco country and Monaco = Munich = Muenchen are both named after monks. (Well I'm guessing for Munich, on etymology.) The Latin was monachus, which gives Italian monaco. The Old English was munuc, and I'm guessing the Old High German was much the same, giving Munken = '(something of) the monks'.

The Grimaldi family seized Monaco in the 1200s sometime by disguising themselves as monks. I don't know whether it was called Monaco before that.