Our business is called Pavilion Broadway, which is a distinctive nod to the area that our first store was opened in. Something we frequently come across on Google is a small coffee shop in London called "Pavilion," which is at "Broadway Market." It's impossible to plan around this kind of thing since our business name is unique, but of course, people will happen to search for the other business and inadvertently arrive at our site. The best advice I can give you is to thoroughly research your business name on domain sites and with synonyms. Think about how your business will appear on Google, and whether it represents exactly what you're selling. It's also worth conducting some third party research into whether your business name resonates with customers.
Finally, when thinking about international expansion, always consider how it will be translated or perceived in other territories. We have all heard about the disaster cases where large companies haven't researched the local market and launched a brand that is culturally offensive or just plain wrong.