Apparently “W” was originally written as “uu” as early as ~600AD, hence the name, however it still used Latin/Roman letters which hadn’t yet distinguished between u and v as letters. For at least 700 years, u and v appear to have been considered the same and interchangeable (so "Double U " could look like “uu” or “vv”) but it depends on your language whether it was verbally called a “U” or a “V” until the first recorded distinction between the two in a Gothic era alphabet written in 1386. The two apparently did still see some overlap in use until about the 1700s with the turning point appearing to be when the distinction between their capital forms was accepted by the French Academy in 1726.
tl;dr: “Double U” predates the distinction between “U” and “V” so it’s up to chance which letter a language called it before it stuck.
I was part of a campaign that was running for a few years that unfortunately ended abruptly before I could ever naturally reveal the several puns and references I packed into my character from the outset. The set up for the ones I remember are my character was a large, friendly paladin whose highest stat was in Charisma, who largely wanted a group of friends and his highest goal was to be called their pal, who wanted to be called by his last name by his friends, who was half angelic/celestial (can’t remember the name of the race), who had dark skin, a large muscular frame, bald head, and short facial hair, whose starting gift was his blessed chainmail, and whose name was Cronwier Aderb.
The references that I remember are that he was designed in the image of a meme with Terry Crews photoshopped as a paladin (stats also reflected this meme), his blessed chainmail was his Hole-y Armor, I remember there being something about his name reflecting a crown but I can’t remember the pun or reference, and lastly he wanted his friends to say “this is our pal, Aderb.” That last one I remember I specifically came up with after the DM asked if my character was going to be “like your dark souls character, another paladerp?”