For the first two years of his life, Number-kun did not even have an official name.
Instead, he was often referred to as postal boy, among other nicknames. Nothing was set in stone. He was just a cute boy who wanted to help you send letters.
Then, after a public poll in 1968, four days after he became the official mascot, he was officially named Number-kun.
In Japanese, this was interchangeable written as ナンバー君 or ナンバーくん. Both of these mean the same thing.
The name Number is because he. The -kun part is an honorific, like Mr., for boys and young men.