You can read here: https://en.wikipedia.org/wiki/Katherine. It is normally a short form of Catherine - though there are various spellings. You must decide if you think its a good name, given its associations. I think it is fine.

It's a good name. It doesn't really mean anything. This seems to be a big difference between Chinese and English-speaking cultures. There is probably a meaning for Cathy and I could look it up, but people aren't generally aware of it. I can introduce myself to people as "Daniel Smith" and they do not think of "Daniel" as meaning "God is my judge," or "Smith" as meaning "an artisan who shapes metal on a forge." Cathy is short for "Catherine." Catherine is a common, pleasant, familiar woman's name. There are lots of Cathy's and Kathy's. In the U.S. it's used by women of all religious and national background. It is a Christian saint's name, and as luck would have it, the Catholic church in my town is "St. Catherine's." In Massachusetts, if we only saw the name we might guess that it was Irish-American, particularly if it were joined to an Irish surname: Catherine Donovan, Catherine Callahan. Obvious I would not interpret "Cathy Zhang" or "Cathy Xu" as Irish! (And just for fun I tried a search and there are many real people living in the U.S. named "Cathy Xu" and "Catherine Zhang.")

It's a normal name for females. It might be a little dated, like Tammy, but it still sounds good.