If there business name is trade marked, yes you will be in a lot of trouble. You will be sued.
I am not sure where you are in the world, but in Australia there are government websites you can go to to check what businesses have been trademarked/copyrighted or registered. Rather than going on google - which is every business in the entire world so it's not very accurate if you can use that name or not. If the business name is only registered - it means you can still use it but make sure YOU trademark it, before they do.
If you find someone over seas with the same name, usually they are only registered to there country unless they are a huge global company. Which is why google isn't much help as all business show up.
If you are in Austraila, you can contact me if needed and I will show you the websites I used (not sure if you can message me on here?) If you are not in Aus, try and find someone who has already started a business and trademarked there business name and ask them.