The UN decides mostly, when it relates to humanitarian and human achievements, like "International Day of Women Judges", or "International Day of Zero Waste", or "International Day of Biological Diversity".

For international days for [fauna], it depends. Sometimes it's created by a person who has worked with certain species extensively or by well known advocates, or it is created by animal welfare groups. For example, World Animal Day was created by Heinrich Zimmerman in 1925, a cynologist (dog scientist, simply). Colleen Paige created International Dog Day, Mutt Day, and Pet Day.