Registration of a different category from an existing trademark name will generally not be rejected. Registered trademarks in one category are only protected in this category and similar categories. According to my country's "Trademark Law"

Art. Article 57 Anyone who commits any of the following acts shall infringe upon the exclusive right to use a registered trademark:

(1) Using the same trademark as the registered trademark on the same product without the permission of the trademark registrant ;

(2) Without the permission of the trademark registrant, using a trademark that is similar to its registered trademark on the same product, or using a trademark that is the same or similar to its registered trademark on similar products, may easily lead to confusion.

Unless it is a well-known trademark, well-known trademarks can be protected across categories according to the Trademark Law. According to Article 13 of my country's "Trademark Law"

A trademark that is well-known to the relevant public shall be protected. When someone believes that his or her rights have been infringed upon, he or she may apply for well-known trademark protection in accordance with the provisions of this Law.

If a trademark applied for registration on the same or similar goods is a copy, imitation or translation of someone else’s well-known trademark that has not been registered in China and is likely to cause confusion, it will not be registered and its use will be prohibited.

If the trademark applied for registration for different or dissimilar goods is a copy, imitation or translation of a well-known trademark that has been registered in China by others, misleading the public, and causing the interests of the registrant of the well-known trademark to be potentially harmed, Registration is not allowed and use is prohibited.