This should probably be asked in the Sofware forum??
Anyway, first up, ensure all your roms are in the goodtools names.
Zsnesw should rename the snapshot according to the name of the rom plus a date and time value if you have it set to save using png format.
e.g. AAAHH!!! Real Monsters (U) 2003 06_10 17-44-54.png
To save in png format, load up a game in Zsnesw and press F1 to bring up the snapshot menu. Change the format to png with the bottom option. You'll only have to do this once, and it will be saved as the format to be used everytime.
You can then use a file renamer program to remove the date and time at the end of the filename.
You can also have the save games and screenshots saved in a separate folder (making it easier to manage if you have lots of roms), by changing the "SaveDirectory =" option in the zsnesw.cfg file.
Also, be aware that if you are using Mamewah to launch each game, you will need to use Long filenames or the resultant snapshots will also use short dos filenames.