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.