To obtain a national trademark, you register it with the competent body in the relevant country. This can be a sensible option if you only operate in one or a small number of countries outside the Caribbean Netherlands. However, the costs and time involved can increase considerably if you operate in several countries, as you will need to go through, and pay for, a separate procedure in each country. What is more, communication with each national office is usually in the official language of that office, and it is sometimes mandatory to have a local representative or postal address.
If your business operates in the Netherlands, Belgium and/or Luxembourg, you have the option of applying for a Benelux registration. BOIP registers trademarks for the Benelux territory.
If you are interested in registering for other national trademarks, you can contact the competent bodies in those countries.
If within six months of filing an application, e.g. in the Caribbean Netherlands, you file an application in another country, you can claim the priority of the initial application for the subsequent one. The protection afforded by your application in the subsequent country will then run from the same date as your initial one (the filing date).
Thankfully, more and more countries are becoming party to the international agreements that facilitate acquisition of trademark protection. If you operate in a relatively large number of countries (or intend to), an international trademark or an EU trademark may be a better option for you than applying for national trademarks.