Puppy uses JWM (Joes Windows manager) as windows manager. You can adapt JWM to your needs. If you want to change the program-menu follow these commands:
Start the program "Menu | File managers | puppyROX file manager"
Change to the directory /root
Click on the symbol "Show all files"
Right-click on the file .jwmrc and select "Open As Text". The .jwmrc-file is opened with Geany text editor now.
Edit the file. The file .jwmrc has the following structure:
Save the file and quit Geany.
Restart JWM: "Menu | Shut Down | JWM restart"
Hint: installing a new PetGet program rebuilds your programs menu automatically. This will overwrite your personal settings, so if you want to keep them, backup your /root/.jwmrc file beforehand and restore the settings after the installation.
You can find further information about JWM on these Internet sites: