Generally speaking, the ships' class is named after the first named ship in the class. It would certainly be a new direction based on a character. At least it is nautical.
The above linked cruise blog is not an official Disney blog. So, their characterization of Triton as a designation of "class" and being "confirmed" are... shall we say, not official. The Cape Canaveral plans called the ship a "Triton Class," but that may be simply because they were just assuming that from the preliminary name.
In fact the document they post on their blog says very clearly under the word "Triton" the designation ("preliminary")...
With a cursory internet search it seems DCL doesn't use the "class" labels. Their first ship was a custom job and simply named "Magic."
The second ship was similar in gross tonnage (~84K) called "Wonder."
The next two were a step up at ~130K GT, the "Dream" and "Fantasy."
They have three in the pipeline being built all at 140K GT, none of them with names yet, nor official "class" distinctions.
Additionally, that same blog site said they got a tweet saying a DCL rep was calling the three new ships "Trident Class." A mishearing? <shrug>
I've seen a few travel agencies sites attempt to create classes with using "Magic/Dream Class" or "Classic/Dream Class" to distinguish the first two lighter ships from the newer heavier ones. But, Disney makes no such distinctions on its own website.
So... with the first four ships called: Magic, Wonder, Dream, and Fantasy; the next three can continue that ephemeral naming system (Wishes, Adventure, Frontier, Charm, etc...). Or, it can go with Triton and more nautical names (Mermaid, Big Blue Ocean, etc...).
