There is no exclusive right to the product name, it is just a common name. It can be put on the label without registration. However, be careful not to infringe the trademark rights of others.

Trademarks approved and registered by the state are "registered trademarks" and are protected by law. Trademarks protect trademark registrants by ensuring that they have the exclusive right to identify goods or services, or to license others to use them for remuneration.