An Etymological Dictionary of the German Language/Annotated/Finne
Finne (1.), feminine, ‘fin,’ first occurs in Modern High German from Low German finne, Dutch vin, ‘fin’; first recorded in the Teutonic group in Anglo-Saxon (finn, masculine, English fin), hence it cannot have been borrowed from Latin pinna, ‘fin of the dolphin, feather.’ No Teutonic word can be proved to have been borrowed from Latin before the period of the Old Teutonic substitution of consonants, i.e., before the beginning of our era (see Hanf). Hence Anglo-Saxon finn must be assumed as primitively cognate with Latin pinna. Is it, like penna, based upon pesna (Old Latin)? If it were based upon *pis-nâ, ‘fin,’ it might perhaps be regarded as cognate with piscis, Gothic fiska- (fis-ka), ‘fish.’
Finne (2.), feminine, ‘tumour, scrofula,’ from Middle High German vinne, pfinne, ‘pimple, foul rancid smell’; compare Dutch vin, ‘pimple.’ The relation of the initial sounds is not clear; Middle High German pfinne points to Gothic p, Dutch vin to f initially; perhaps the double form is due to confusion with Finne (1.); p may be the correct initial sound.