I think it will be important to find a standard definitions for the administrative divisions.
Now in the database there are names like 'State of New York' or 'Toscana' or 'Michigan'.
Of course when someone use the adm1 or adm2 lists the results is not very nice to show.
According to me the best solution it will be to have in the alternate name a record with 'Official name' just with the real name like 'New York' because as is a ADM1 of course we can understand is a State.
Eventually could be a extra field for the division name with example 'State of' or in italy 'Regione'