There are many theories on why Bill became a nickname for William. The most obvious is that it was part of the Middle Ages trend of letter swapping. Similar to how Dick is a rhyming nickname for Rick, Bill is a rhyming nickname for Will. Since hard consonants are easier to pronounce than soft ones, some believe Will morphed into Bill for phonetic reasons. Interestingly, when William III ruled over England in the late 17th century, his subjects mockingly referred to him as “King Billy.”

Source: Zephyrus