My name is very hard to pronounce, even in my own country I have to introduce myself several times and it is always spelled wrong. China is my third time abroad for a longer time. When I arrive I use my own name and see how that goes. In the US and France my friends came up with nicknames, some random nicknames, some sound like my real name. Sometimes I use a different name (middle name or first two initials of my name), just makes it easier.
It seems most often the English names Chinese use are just chosen, or perhaps given, and have nothing to do with their Chinese names. Sometimes, though, they choose names that are close in pronunciation to their Chinese names (as close as it can be, anyway), and I've even seen them create names that just sound close to their Chinese names but aren't actually real English names at all. This can make for some odd sounding names, but I think it's a neat idea to make up your own unique name.