It is unclear what exactly is being referred to by “purity,” so there are several possible answers to this question depending on context.
If the question refers to the concept of purity in general, then there is no single owner or authority over the concept. The concept of purity is an abstract idea that is defined and valued differently by different cultures and individuals.
If the question refers to the Rice Purity Test or the Innocent Test, then there is no single owner either. These tests are freely available online and are not owned or copyrighted by any one person or organization.
However, if the question is specifically about a product or brand called “Purity,” then it would depend on what type of product it is. “Purity” is a common name used by various companies for products ranging from water filters to skincare products to food and beverages. Each of these products would have a different owner or manufacturer. Without further information, it is impossible to determine who specifically owns a product called “Purity.”