Many people just use the standard Chinese transcription of their English name as their Chinese name. For example, Michael is迈克尔 (mai4 ke4 er3), & David is 戴维 (dai4 wei2). The name Nancy in Chinese is usually written as 南希(nan2 xi1), which means "south hope". You can check out this website if you're curious what your own name would be.
Since this is one of the few opportunities I'll have in my life to choose my own name, I thought I might get a little creative & use the characters 南西 instead (still pronounced nan2 xi1), meaning "south" & "west". Since I'm from the southwestern part of the US, I thought it would be appropriate.
My Chinese name doesn't technically mean "southwest", however. To say the word "southwest" in Chinese, you invert the directions, saying 西南(xi1 nan2) "west south". Northeast becomes "east north" in Chinese, & so on. So I was surprised to see this street sign with my name on it in Qi Bao, a little canal town on the outskirts of Shanghai.
It's a strange street sign because to say "Nanxi Street" in Chinese would be like saying "Westsouth Street" in English - it just sounds weird. I can only guess that this must be a deliberate choice for the name of this street. Maybe there is another南西 out there somewhere, a kindred soul.