The word Fotze (cunt) has the irregular spelling Votze, which is usually explained as a reference to the denotated part. But comparing Vater (father), I don't know any reason why hat wouldn't be Fater. In many cases, word initial V is homophone with F. While Vogel (bird) may be in reference to the simplified drawing of a bird, too (hence Vogel-Vau as mnemonic for the letter). Otherwise initial V exists only in loanwords, I guess. Vagina (sheath) is decidedly not pronounced Fagina (though the allusion to lips might lend itself to a word play on eating ...), perhaps (sound-)symbolic.
So, why is V such a very vveird letter in German, for lack of a better word?!