There is no universally accepted single "correct" way to transliterate names from Arabic or Persian into the
Roman alphabet. So there is no reason to think that Ferid cannot be simply an alternate spelling of
Farid.
My Turkish name dictionary (
Adlarimiz by Aydil
Erol) doesn't include Ferid, but it does have the female name Feride as well as Feridun. So Feridun is a spelling of
Faridoon used in Turkey.