The problem of non-referring names has a lot in common with the notion of the ‘willing suspension of disbelief’ in connection with theatrical productions.
The sand trap of inferring existence from reference is a widely-used propaganda technique.
Here is a mathematical model for names.
Definition 1. A name is any monotonic collection of sets, whose union is uncountable.
Definition 2. A referring name is one whose collection has a nonempty intersection.
Definition 3. A close referring name is a referring name whose collection is finite.
Remark 1. Close referring names refer to things in the immediate environment.
Definition 4. A distant referring name is a referring name whose collection is infinite.
Remark 2. Distant referring names refer to things outside of the immediate environment.
Definition 5. A non-referring name is one whose collection has an empty intersection.
Remark 3. For example, ‘Pegasus’ is a non-referring name.