Well, no. Rosenbaum discusses μυοχάνη on pg. 14, a word found in Galen's Glossary of Hippocrates. Galen:
μυ<ρ>ιοχάνη· ἐπίθετον χασκούσης. εἰ δὲ μυριοχαύνη γράφοιτο, ἡ ἐπὶ μυρίοις ἂν εἴη χαυνουμένη.
My trans. "Muriochane/Muiochane: A name for a woman yawning. But if it is to be written 'thousand relaxer', it should be a woman who relaxes [ie., her legs] for a thousand."
This "yawn" or "yawn after something" can be similar in Greek usage to our "drool after."
The "Cleopatra" claim is internet garbage, nowhere in Rosenbaum, and I wonder if an AI summarizer picked it up from Reddit or something? All Rosenbaum does is quote Erotian in that discussion, who says "μηριοχάνη ὄνομα γυναικός," Meriochane is the name of a woman.
There's another related word from the Suda, μυσάχνη, which it attributes to Archilochus as a reference (name for?) a prostitute.