The character Myrrhine, a young and sexy wife, appears in the bawdy comedy-drama Lysistrata by Aristophanes.

One web-source, authored by a professor, states that the various character-names were not simply names: they had meanings in ancient greek, the name Myrrhine being a sexual reference to a part of the female anatomy.
http://www.humanitiesinthebeginning.org/Hum211/greece12.htm; final paragraph

The professor, being professorial, uses a technical term to specify that part, but I suspect that Aristophanes would in fact have used the more earthy, "street-language" of his day. On the other hand, a friend with whom I discussed this felt that the name Myrrhine relates to myrrh.

To check further I contacted a friend in Athens who is a by profession a Greek-English translator. Her reference-books indicate that the word indeed refers to the part of the female anatomy.

HOWEVER, there remains the possibility that there was, in greek, a linguistic connection between the anatomical word and the substance myrrh. Here my research ends except to note, in support of a possible such connection, that the substance myrrh was used as a base for fragrant oils and perfumes (see definition in bartleby).

Post-edit: boldfaced added to highlight the tie to the subject of myrrh, per of-troy's question.