Forgive me - this hurts a little. Aside from the lyrics.
I do not know many evident facts about this maybe-historical character. But definitely I dare to state that neither he nor his contemporary fellow human beings were native english speakers.
That is: his christian name was certainly not William and you can bet that nobody ever considered calling him "Bill".
Today, as a switzerman, your original language is either french or german or italian, read from upper left to lower right (I hope to not insult any muslim by this).
In french his name is tradited as "Guillaume Tell" (g-ee-oh-m), in german as "Wilhelm Tell" (vill-hell-m) in italian "Guillermo Tell" (g-ee-yerr-moh according to what little I know about italian, sorry).
Only the german version sounds a little like "William". BTW, nobody named "Wilhelm" will be addressed so in Germany, evreybody will call him "Willi". Sic. Don't know how the french and italian are handling this.
IMO one should not try to translate everything. Especially names - what would an US citizen think about e.g. a newspaper from Munich referring to some "... president Schorsch Busch ..."?