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[Star Wars - The Mandalorian] Is the Razor Crest the ship's name or class/model?

Is Din's ship named the "Razor Crest" or is that the ship's model, ala yt-1300? I feel like characters in the show have referred to it as "a razor crest" but other times more as the ships name, and outside sources seem to refer to it as a name.
gpt
It's heavily implied to be a Razor crest model gunship. Pre-imperial regulation. Din doesn't seem to care to name his tools personally and keeps some level of detachment from his equipment. For something to be named it must be worthy of a name by deed.

Granted the only indication that it is a model and not a ship name is the character from the first episode naming it as such and the lego tie in set naming a razor crest model gunship.