Hello Michael,
Try as I might, I can't find a NAAFI badge in my collection or on the net!! Quite simply, it was a red circle with NAAFI in it.
HMS Petard was quite new when the incident that you are researching took place, being laid down in December 1939, launched in March of 1941 and completed on the 15th June 1942. The issue of tallies with just "HMS" is fairly complex in the early stages of WW2, being issued to boarding parties, men going on leave and joining new ships and were to be returned on rejoining or joining their ship. Admiralty Fleet Order (AFO) 4678 of September 1942 stated that even with stocks of named tallies being available, "HMS" tallies were now to be issued only and were to be worn ashore at all times. Named tallies could still be worn whilst at sea. From March 1943 only tallies with "HMS" were to be worn at all times.
So to answer your question, yes there would have been "H.M.S. PETARD." tallies, but she was around for a fairly long time, so there would be a few different weaves
http://www.britishbadgeforum.com/for...ad.php?t=39767 She was finally broken up in 1967.
Sorry to be so long winded, but I hope this is of some help.
Andy