1. What if I use a taken name for my game studio/website/company if I could go that far?
2. What if I use a taken name for my game (having the same name with a brand/company/... or with other game)?
Are these names used locally? or are they businesses from different countries?
It's important to check with an attorney and vet where these names have been registered specifically.
Of course, this is impractical if the business or product is registered in any country that is part of your target audience (at which point you may need to operate under different names in different areas, which is particularly annoying).
You'd be surprised however to see just how often names are only registered in one country (of origin). Some ill-intentionned trolls may lurk about, see something succeed, and quickly register that name of operation in other countries.