Can LLC expand into another country with same name and what tax complications there will be?

I have a LLC and for day to day tasks I have hired a few people from another country. I am thinking to establish an office there so these employee can work from my remote office. So the question is, can I start a company in another country with the same name as my American LLC? If yes then what tax complications there might be or how will I be reporting this office in my tax return.