"
Falsetto" is what I would fully endorse, too.
Technically,
falsetto is an Italian word, used commonly in English since (to directly answer your question) there
is no single word that defines capability of singing both male & female ranges. However,
falsetto, defined in English as "head voice," is widely known in the musical community as a person's ability to increase tension in their vocal chords which results in a full octave (or more!) higher pitch in tone. Both men and women are capable of this, but the contrast is more drastic among men and is regarded as
highly effeminate but also
remarkably fun.
For example: ever heard a song by the Bee Gees?
I'm extremely enjoying this work, btw. Thank you for sharing~