Are there countably many names? Countably sayable, perhaps, but I don't recall seeing any limitation to word length in the spec. See: "Below is the full 189,819-lettered word for 'titin':" at https://cw39.com/wp-content/uploads/sites/10/2020/09/longest... as an example.

Surely if we can have a 189,819 lettered word we can have a million billion trillion lettered word or an uncountably lettered word. They'd be used in the same way as the really long numbers in that we'd give them some other handier name that collides when not given context. e.g. In spoken language pi/pie are often confused if the conversation does not already have a mathematical context and no one says 3.1415926535... conversationally just as no one uses the lenghtier version of chitin and no one would use the uncountably long name for some uncountably long number.