Init is the first process started during booting, and is typically assigned PID number 1. It is started by the kernel using a hard-coded filename, and if the kernel is unable to start it, a kernel panic will result. Init continues running until the system is shut down.
Puppylinux uses the Busybox init process.
"BusyBox combines tiny versions of many common UNIX utilities (GNU fileutils, shellutils,textutils) into a single small executable. It contains a small init system, which is a strippeddown SysVinit scheme. It can read an inittab file, but does not support runlevels" -- Yvan & Frénot, A Survey of Unix Init Schemes 
The name of the process is
The first script that his process called is referred to as the sysinit entry point, and it is defined in the file:
::sysinit:/etc/rc.d/rc.sysinit tty1::respawn:/sbin/mingetty --autologin root tty1 tty2::respawn:/sbin/getty 38400 tty2 tty3::respawn:/sbin/getty 38400 tty3 ::ctrlaltdel:/sbin/reboot
and from inspecting the above script we see that for puppylinux the sysinit entry point is:
More Information on the BusyBox init system can be found at: