It's possible to have a single given name rather than the more typical two-word deal. So 'Chun Li' is a plausible full name, with 'Chun' as the surname and 'Li' as the sole given name. Or vice-versa. It'd just be somewhat rare.

> It all gets
>very confusing if you poke at it too much. I'm pretty far out of my
>depth when it comes to spelunking the secret depths of Chinese naming
>conventions.

Honestly, this is one of those things that a non-speaker can just relax and let slide. Lots of rules, yes, but there's also exceptions to each. My own name combines two entirely different Romanisation systems in one linguistic trainwreck. It's pretty hard to go wrong when even Chinese parents themselves don't worry about the details.