Why is it OK for a chinese person to give themself an 'English' name?
well, actually, sometimes it isn't.
It could be that they see it as a smoothing-over courtesy, given that those who do this are generally choosing to work in a first-world, 'white' society.
Two things come to mind.
I was working in Australia many moons ago. Due to a HCP shortage, a few people were taken on who took far longer to ease out of post that to put in, shall we say.
A HK Chinese person arrived, and given the multicultural reality of most workplaces, everyone made her welcome. But it all got rather strained when it came to her name, written (by her ) Ah Hong. So we all said Ah Hong. But we weren't ready for the fury as 'Ah Hong' is a boy's name, hers was pronounced A(i)h Hong, a bit like the Scottish 'Aye'. Just tell us, don't go to HR!!
She did actually remain and become a solid member of the crew....
Then along came let's say Annabel. Chinese young woman. My given name is, let's say Annabel, but everyone calls me Anna. For 8 years by then. She walked straight up to me, week one, and told me that it would be less confusing if everyone called her Anna, and me Annabel.
Er no. You've chosen that English name. Your actual name is Chinese- that you think us whiteys couldn't possibly pronounce.
My name is Annabel! First dibs on Anna! 