An Etymological Dictionary of the German Language/Finne
Finne (1.), f., ‘fin,’ first occurs in ModHG. from LG. finne, Du. vin, ‘fin’; first recorded in the Teut. group in AS. (finn, m., E. fin), hence it cannot have been borrowed from Lat. pinna, ‘fin of the dolphin, feather.’ No Teut. word can be proved to have been borrowed from Lat. before the period of the OTeut. substitution of consonants, i.e., before the beginning of our era (see Hanf). Hence AS. finn must be assumed as primit. cognate with Lat. pinna. Is it, like penna, based upon pesna (OLat.)? If it were based upon *pis-nâ, ‘fin,’ it might perhaps be regarded as cognate with piscis, Goth. fiska- (fis-ka), ‘fish.’
Finne (2.), f., ‘tumour, scrofula,’ from MidHG. vinne, pfinne, ‘pimple, foul rancid smell’; comp. Du. vin, ‘pimple.’ The relation of the initial sounds is not clear; MidHG. pfinne points to Goth. p, Du. vin to f initially; perhaps the double form is due to confusion with Finne (1.); p may be the correct initial sound.