Does anyone know how to check if a business name is trademarked or not?
It's a name for a business that I plan to use online, so it would have to be ok to use internationally.
When you register a Trademark with the Irish Patent Office you have the option of registering an international Trademark. All countries that are signatories to the Madrid Protocol will then honour it. That includes all of the EU. I'm not sure about the USA and the rest of the world.
Unless the business that uses your name is based in the EU then forget about taking them to court to defend it. It's a protection but you'll need deep pockets to defend it.
Your best bet is a good search of the Patent Office's website.