I'm slightly uneasy with this change, because it claims that objects have members, but we often discuss properties at the level of the type here, not at the level of a specific object.

I think the uneasiness is ultimately due to the term being inappropriate -- "anonymous union object" makes sense for namespace-scope or block-scope anonymous unions, but at class scope we're not defining an object. I wonder if it would be better to define the term "anonymous union member" in [class.union.anon] for the class-scope case.

Maybe something like this:

A union of the form

union { member-specification } ;

is called an anonymous union; it defines an unnamed type and an unnamed variable or non-static data member of that type. A non-static data member of anonymous union type is called an anonymous union member. An object of anonymous union type (either an unnamed variable introduced by an anonymous union declaration or a member subobject corresponding to an anonymous union member) is called an anonymous union object.

... though we'll need to check through the other references to "anonymous union object" to see whether they need changing too.

What do you think?

Sounds better, although we tended to avoid "anonymous union member" in the past because of ambiguity: a member of an anonymous union, or a member that is an anonymous union?

Editorial meeting consensus: not a net improvement.