According to my local chinese person, most likely their chinese name is "Lei Ming", as "Lei" is more likely to be the family name (which goes first in Chinese, and many other east-asian cultures). "Ming Lei" then is also a westernised version of their name, with the order changed to our family-name last - to avoid the hassle & confusion east-asians have when they try to use their "native" name in the West, and "Tony" is a western name they've adopted, cause us westerners never seem to be able to remember chinese names.
Another name difference tween east-asia and here: they pretty much always use full-names. They don't drop family names when they call or refer to each other, as we often do - not even within families. I.e. there pretty much is no 'familiar' name. E.g. you pretty much wouldn't ever refer to "Lei Ming" of this article as just "Ming".