Pretty much every family I have researched as part of my family tree had a William at some point. It would have been more compelling if the name was more unusual.
Which reminds of a personal anecdote - I was contacted last year by a DNA match that was somewhat close (in the 2nd cousin range). She told me that her grandfather was raised in an orphanage and they never knew much about his family background. She sent me a copy of his birth certificate that indicated he was "illegitimate" and his father's name was left blank. Because I have researched my family tree up and down as well as sideways, as soon as I saw the place and year on this birth certificate, I knew exactly how we were related. My grandfather had a loner brother named Walter who never married and even his obituary said he had no family. He lived in Lima, Ohio and was literally the only person in my family that ever lived there. This DNA match's grandfather was born in Lima, Ohio. And his name was Walter. I then verified all of our shared matches with the right lines of the family. So my grandfather's brother had indeed impregnated a woman out of wedlock. I will never know if he knew he had a son or if it was just a one night stand, but the fact that she named her son Walter after him seemed significant. The cool thing is that opened up a whole new line of the family for me that I never knew existed. I'm now Facebook friends with my newfound cousin (technically we are 2nd cousins, once removed), which is pretty cool.