The iPAQ is a PDA originally manufactured by Compaq, and later rebranded as HP when Compaq were purchased. It's not an abbreviation, more a shortening of Compaq, in the same vein as iPod?. No one can really agree how to capitalize it.
The native operating system on these is MicrosoftWindows CE, now known as "PocketPC", but you can install Linux on them. The main distribution of Linux is called Familiar, and just like on big brother PC Linux, there are two major competing DesktopEnvironments for Familiar: