How do I kill a nameless process that won't die?
Things to try:


check info button in Activity monitor - it may show you what this process actually is
if it's spawning new processes, that looks like something got stuck in infinite loop
you can also check the sample of the process (in Activity Monitor click on System Diagnostics Option -> Sample process
if you have such rogue process and are unable to kill it reboot should help (unless that is some malicious app doing it on purpose)
if none of the above helps and you've installed some new app recently, try to uninstall it, reboot, check if it's still there and maybe reinstall
check system.log (it's a regular file, you can check it using Console.app, or any other terminal emulator app) - you can do 
cat /var/log/system.log
or start this command and check what is being logged:
tail -f /var/log/system.log (Ctrl+C to stop)