“ANSI C” by Kernighan and Ritchie disagrees , including that syntax (note : retranslation from Polish as that’s the language my copy is in) :

A8.3

[…]

struct-union-specifier:
, union-struct identifier ₒₚₜ { compound-declaration-list }
, union-struct identifier

[…]

Specifiers of structures or unions with [a compound declaration] list, but with no label [identifier], creates a unique type; it may only be referred to in the declaration in which it is part.

Unless I’m misunderstanding something, I’m pretty sure they’ve been standardized in C11. Also mentioned here.