Trademarks, trademarks approved and registered by the Trademark Office are called registered trademarks, which are protected by law and enjoy nationwide exclusive rights.

Product name is a common noun, such as basketball, football, toothpaste, etc.

Any trademark that is distinctive and does not infringe the prior rights of others can be applied for registration and used on goods of the registered product category. The international classification of trademarks is divided into 45 categories, each category corresponding to goods or services such as football, basketball, toothpaste, etc.

Like "Naisi" on toothpaste, Naisi is distinctive and has no prior rights. If the Trademark Office approves the registration, then it becomes a registered trademark.

But if I want to register "Big Football" on football, that won't work. It has no distinctiveness and no easily identifiable function.