There is not a country in the world where registering a trademark is a requirement by law.
No one or no place can make you do this.
The only purpose to registering your trademark is to protect yourself and your company's reputation from those that might capitalize on it.
A good example of not registering a trademark in all the present and future markets that a company might be moving into in the future is the story of Budweiser and Budvar.
When Budweiser was first brewed, the company owners did register their new trade mark with the USPTO.
Nineteen years later a little brewery in the Czech town of Ceske Budejovice started to make its beer.
In the German language the translation of this town and the beer was Budweis.
This beer is called Budvar In 1911 the two breweries became aware of one another at a trade fair and made an agreement to stay out of each other's chosen markets.
This worked until the fall of the Berlin Wall and the expansion of both breweries.
Since that time both have basically invaded the others markets.
While it is true both are registered trademarks in their respective countries and markets, the battle is on for where both wish to expand too.
The makers of Budvar have admitted they have financially benefited from the reputation of Budweiser, but that does not entitle them to sole possession of the name Bud.
Luckily the brewery that makes Budvar is state owned and is not for sale at the present time.
Until that changes, there will be two types of Bud beer for sale for the consumer.
By registering a trademark with the Treaty of Madrid in 1891, would have avoided this entire mess.