I honestly doubt that most ships received proper names in their early developing cycles at all. Especially in a post-apocalyptical scenario resources probably aren't that obtainable, and thus any built ship has to be modified to fit its environment the best (e.g., deserts, alpine landscapes and such). Sailing the sea is one thing. The sea, well, remains the sea. Flying low-altitude however surely requires less subtle changes to a boat's design. I could think of a CQB-Squid for urban combat or something the like. So, even with certain designs being superior, those would still have sub-designs. I'm thinking about it like the early submarines were named. During the Second World War, German submarine classes ranged from Type I to XXIII, not containing any names at all. Those then received further sub-classes, as II A, II B, II C and II D. Even the Type VII, the workhorse with its main-type ending up being VII C, never received any change to something more recognizable. Similarity can be found in U.S. history, where the class of the most-built submarine during the First World War was simply called S. According to Wikipedia (our beloved, never-failing source for trustful knowledge *cough*) those S-class boats sometimes received the name Sugar Boat, what I would take as the equivalent of the class names we are using in GOI.
Our problem with the Galleon is fixable by just this pattern: the first submarine fully designed and built in China (meaning without being a copied U.S. submarine) was the Song-class, in 1997. This name, however, is only the classification the NATO gave to it. The Chinese name for the class is Type 039, separated also by letters, e.g., Type 039G.
If you put the pattern of boats driving below sea-level on ships flying above, we could easily get something like FW 42-A for the first Galleon (FW being the abbreviation for flying whale... I'm not always in a creative mood). But that, alas, doesn't really sound attracting nor fearsome enough for a game, does it?