Process name from its pid in linux

On linux, you can look in /proc/. Try typing man proc for more information. The contents of /proc/$PID/cmdline will give you the command line that process $PID was run with. There is also /proc/self for examining yourself :)

An alternative (e.g. on Mac OS X) is to use libproc. See libproc.h.

There is not any general way to do this unix.
Each OS has different ways to handle it and some are very hard. You mention Linux though. With Linux, the info is in the /proc filesystem.
To get the command line for process id 9999, read the file /proc/9999/cmdline.