木木 is there anything linked to a Chinese superstition with this double character?
Thank you for your thoughts. 
Well turns out it wasn't some Chinese superstition; it was sort of her own; this is how she explained it finally:
"There is a superstition in China. People want to know his own destiny and what his life is. For example, some are fire, some are water, and some are wood. This is based on his birth date. People who look at their destiny are called  Fortune teller, the fortune teller said that my life is short of wood, so I thought of a name called wood wood, this is superstition This is a kind of superstition in China, similar to a belief In other words, my name is Mumu, which is helpful for my good luck