There is a wiki for the Avatar TV show, though. I searched it for “ship” and found entries for “Zuko’s Ship” and “Azula’s Ship,” but notably, neither of them had proper names. The entry for “warship” describes cruisers, but the only specific ship designation is the aforementioned “Empire class,” and the entry on that again lacks any specific names. It does muse that, if the Fire Nation navy follows real world naval naming conventions, the first ship of that class would have been named Empire, but that’s about it for ship names in the Avatarverse.
It struck me as a little odd that I never heard anyone refer to a ship by name in the series. On the other hand, aside from Fire Navy ships, not that many actual ships played a significant part in the show. There was the pirate–excuse me, “high-risk trader” ship, but not much else.
There were plenty of Fire Navy ships around, though. I’ve got a vague notion that the Navy doesn’t really name their ships. The Fire Nation emphasizes mass production and conformity; maybe the ships are just interchangeable cogs in the war machine to them. Maybe they number them or just refer to them by the commander’s name when they need to talk about a specific ship.
I watched the series several times and a couple of them with the, “Hey did you know” factoids at the bottom of the screen and I can not recall any named ship.
Although Sokka did invent the masterful technique known as the “Airship Slice.” Which was pretty awesome.