I have a friend named Zi, and I think it's a very pretty and unique name for a girl. I would like to use it as a middle name for a possible future daughter.
The first "Zhi (fourth tone)" you have does not actually mean aspiration -- the phrases "Zhi2 Zhi4" or "Zhi4 yuan4" both do, however. Zhi4 alone means "the will (to do something)". [noted -ed]The "wisdom" meaning is also fourth tone. (The numbers after words are the tone numbers.)
TSCH-UY