It depends on where and how you do business
There is no single answer. International trademark law is complicated because every country sets its own rules, and regional groups such as the European Union adopt policies that reach across several countries at once. The rights you hold in a mark stem from the laws of the country where you claim them.
How international agreements and regional groups play a role
Your country's rules can sometimes be influenced by international agreements and economic blocs. The European Union is a good example: its trademark policies apply to every one of its member countries. Individual nations, meanwhile, have their own laws, which are also shaped by regional, political, and economic factors. Ireland's laws resemble those of the UK, for instance, and countries such as the US and Canada recognize service marks.
Our advice before you expand
Start by getting to know the trademark laws and agreements that apply in your home country before you take your business abroad. When you file for a trademark, it is wise to talk with a lawyer, particularly if your company has interests in other countries.