Hi, Ms Jennifer. My first name is Ming too, because for the family book told the Generation Poem that I am in the generation of Ming. Then I can have another character after Ming in my name. If Ming is not a generation name which is fixed to be an exact character, it can be 明 or 茗 or 鸣or 铭， respectively meaning bright, fragrant tea, tweet like a happy bird and inscription engraved to remember or remind. Personally, I like the second one for a girl. Mine is the first one. Hope this helpful.