Not sure if this should be included in the 11th c. theme: the traditional songs you mention are in the world of Broadside Ballads, and while the 11th c. must have had ballads ( though the troubadors were perhaps doing a better job in the following century) I'm not sure anyone's tracked Lily of the West, Banks of the Ohio or "Down in the Willow Garden" that far back.

These were songs that are often enough about crimes because they very often were based on an actual crime, and sold in markets. They were called broadsides because you'd buy a single sheet. Just as certain kinds of stories tend to make news today, certain themes tended to stay popular, and so it's not perhaps surprising that people dying for love , or taking revenge on a mean lover, or being murdered by a lover tend to be well-represented. The words were commonly set to a popular tune ( in the 17th c. Packington's Pound would be a favorite) so that only the words needed to be printed. Broadside ballads could be seen in public spaces- an inn or a barbershop might have a few stuck to the wall, so that patrons would have something to do while waiting their turn for a dinner or a shave.

Once written, however, the ballads tended to acquire a life of their own, dropping verses, gaining others, changing direction. Which helps to explain why there can be a few verses saying very little, then for no apparent reason someone is stabbed. Folklorists sometimes call these early sex education, because there's often someone coming to a bad end because of an unwise romance or ( though unstated) an unwanted pregnancy.

As you can imagine , a few hundred years of matching and re-combining created a lot of variety. Maybe the most well-known effort to sort some of them was done in the 19th c. by Francis Child. In five volumes, Child made an attempt to group some of the various versions together. This has continued. Steve Roud more recently compiled a huge index of ballads, now searchable over at the Vaughn Williams Memorial Library. Search the VWML, and you'll find that Down in the Willow Garden has 28 listings- none going back before 1927, but that's just when someone finally wrote one down.

While the name William is just one of many in the English-speaking world now, if you go back to the 18th c. and before you will find an amazing lack of imagination for first names. John, William and Richard were very common for men. With more than a few men in the same household with the same first name variants were produced that became names in their own right, so Dickon , Dickson or Dixon from Richard; Wilson, Wilcock or Wilcox for William. With that and a high mortality, it's a common problem for researchers to wonder , say, which William Oughtred was getting married in 1742- the son for the first time, the father for the second or the grandfather for the third.