Firstly, I would request the mods to not encourage such personal argumentativeness between members get in the way of proper discussion here on the forum!
secondly
The definition of a frigate has varied greatly over the centuries with a few basic things remaining the same
A frigate is term used for a fast maneuverable lightly armed ship to be used primarily for escort duties and patrolling duties with limited anti-shipping capabilities. in today's age that denotes a ship primarily used for anti-submarine and anti-aircraft escort roles for a CBG or a cruiser battlegroup.
as for the name, well i believe the designation of a ship is primarily a decision to be taken by the operating navy, for example the french have all but done away with the term destroyer referring to their surface combatants as first class and second class frigates, for international norms however they maintain the pennant numbers with D denoting the ships that could be classified as destroyers internationally while F denotes the ships that can be classified as frigates internationally.
I believe someone above has commented on the USN classifying the Truxton, California, Virginia and bainbridge classes as frigates.well again similar to the french these ships actually carries pennant numbers beginning with a C signifying cruiser, for example the Bainbridge was classified as CGN-25.