IMO it's a separate category of modifiers/decorators to the type, like how adjectives and nouns are distinguished, and the only reason we have the false-choice in C/C++ is because it's not alphanumeric (if the token were e.g. "ref" it would interfere with the type or variable name in either other convention).

If I were forced at gunpoint to choose one of the type or name, "obviously" I would also choose type.