I often see this C grammar in books. However it seems <identifier> is never declared.
Am I missing something or is this grammar incomplete?
I can't speak for whether the grammar is complete, but <identifier> is a token (i.e. a terminal), in the same way as e.g. <string> and many others are.
Tokens are not defined in the grammar itself but rather in a lexer specification.
The lexer is a component of most parser systems, which reads the raw input and turns it into a stream of higher level tokens (a.k.a. lexemes) that the parser then consumes.