My old Amarr character's faction ships do carry a HIMS (Her Imperial Majesty's Ship) prefix (non-faction or civilian ships are not worth such of a distinction).
Huh. So I'm not the only one to use this (albeit I use it for most of my "practical purpose" ships, i.e. PvP ships and commonly useful noncombat ships like haulers). Dedicated PvE ships, temporary ships, joke fits, etc. tend to be given quick and/or joking names that don't have a title.
I ran with a w-space corp for several months that used a prefix to quickly id non-corp ships that came into our wormhole system. Worked rather well in that setting because most neutrals/reds coming in would have no idea who lived there and thus couldn't come in with a copied prefix.
Some time ago, I lived in a W-space corp where we actually sent out "IFF codes" to be put in our ship names by mailing list. It worked fairly well, for the most part - aside from a couple of frights when someone forgot to read the mail.
I generally found that if I was in low/null sec, ANY name that indicated RP/Serious Business was like dangling the worlds biggest carrot in front of a legion of angry rabbits. Fleet fight in system? They make instant friends and scream "TRUCE! LETS GO KILL THE LOLRPER!!!"
Amazingly enough, I haven't had this issue (I've been using the HIMS prefix all though my time in Providence, Great Wildlands, and Insmother). To be fair, there were a lot of people who named their ships "USS ______" or "HMS _______" so they may have figured it was just some wierd variation/mispelling of the latter.