Generally, yes. Some countries, such as the United States, require you to use a trademark in commerce before granting a trademark registration. In these “first to use” countries, the first company that uses a Trademark in commerce has the best rights.
Some countries, such as China, grant rights based on the date that a trademark application is filed, rather than the date that products or services are sold. In these “first to file” countries, it is very common for people and companies to trademark brand names that are popular in other countries. If they file before you, they have the trademark rights in those countries.
If you plan on doing business internationally, you should consult with a Trademark Elite Attorney about securing the brand name before bad actors can steal your branding in foreign countries.