The three Australian ships of this have been built in Australia, not Spain. We designate them as destroyers though. The upcoming Type 26 based ships are frigates.
They are rightfully designated as Destroyers at 5,800 tons minimum. Versions go up to 6,100 tons.
But if you’re in a Surface Action Group with Burke class Destroyers at 10,000 tons, I guess you have to take the designation you’re given.
Or properly re-designate the Burkes as the Cruiser they are.