And virility literally means manliness or manhood, and by extension physical qualities ideally associated with men. Romans had another concept, virtue, for manly mental qualities. Ancient Greek "andreia" covered both aspects of manliness.

Andrea as a female name is similar to Carla or Caroline. Take a name that means something related to men (but no longer obviously so) and adjust it a bit to make it a female name. As a male name it just reflects changes in pronunciation over time.