I like Kate better than Tracy. However, I have never understood taking on a new name for a different language. I realize it may be difficult for westerners to pronounce your real name using the correct pronunciation and tones, but I think most people would rather call you by your real name, even if it takes a little practice to say it correctly.

Choose whatever you like. I know that immigrants change their names for a host of reasons. It's really only your business, no one elses. I can't imagine that anyone would say that they prefer to call you by your "real name." How would anyone even know what one's 'real name is?'

Tracy (or Tracey) used to be very popular here in England, though it found favour more with working class people. The Queen would NEVER call a child of hers Tracy! Kate is popular with all classes. We have Kate, Duchess of Cambridge. One day she may be Queen Kate! (Queen Catherine) I feel that Kate is a safer option.

Kate is a much more common name, but you can choose whichever you want.

I like both names. Be aware that Tracy is an old name that is gender neutral nowadays.