What does that mean?
Its usefulness is clearly that, combined with unambiguity , there is a 1-1 relationship between objects and names. This means that comparing two objects for identity is unnecessary -- the equality of the names is sufficient.
In practice, we consider a world with many competing naming schemes, and competing naming authorities. There is nothing to stop a naming authority issuing a name for any object, even itf it already has another name. The properties of a naming scheme or the policies of a naming authority may well define that names are unique, but that can only hold within that scheme and the domain of that authority.
Whether one is discussing unambiguity, uniqueness, or both, the question always arises: when are two objects "the same"? Neither of these properties can be defines without some definition of sameness .
(up to Requirements , on to readability)
Tim BL