Japan definitely chose it themselves. Before, the country was known as 倭国, with 倭 meaning something like harmonic but also submissive. Obviously one Tennō wasn’t too happy about that and began signing letters to the Chinese court as “from the ruler of the land where the sun rises (日本) to the ruler of the land where the sun sets.” So Japan became the “Land of the rising sun” (well literally it’s the “sun’s origin”).