What is the ancient Chinese one-character name for woman like '子’ means man?
The equivalent of 子 for women is also 子. 


  【清·張自烈·正字通】子部：女子亦稱子


Examples from Old Chinese texts:


  【孟子·告子下】逾東家牆而摟其處子，則得妻，不摟，則不得妻，則將摟之乎？



The Works of Mencius: "Breaking into your landlord's house and harass the virgin girl gets you a wife; refrain from harassing and you don't get a wife. Does that mean you would do it?"



  【詩經·國風·周南·桃夭】桃之夭夭，灼灼其華；之子于歸，宜其室家!



The Classic of Poetry: "Forests are green and flowers are red; a girl is marrying, and she'll make her new family happy."




In ancient Chinese, 女 either meant "unmarried woman" or "you". The character for the latter usage became 汝, but is still printed as 女 in many modern publications of ancient works.