The “V” in V-J Day stands for “Victory” in the phrase Victory over Japan Day.
The name describes the Allied victory over Japan at the end of World War II. It parallels V-E Day, or Victory in Europe Day, which marked Germany’s surrender in May 1945. “V-J Day” was also called Victory in the Pacific Day or V-P Day in some contexts.
The term is used for more than one date because Japan announced its surrender in August, while the formal surrender ceremony took place in September. In Japan, the announcement was broadcast on August 15. In the United States and other places west of the International Date Line, the announcement was heard on August 14.
The wording is therefore a historical label rather than the name of one universally fixed calendar date. The phrase identifies the victory over Japan, while local usage determines whether it refers to the announcement or the signing.