I had no problems just registering the CompanyName in my country. There was no other companies using any other variation of the name I chose though, so I didn't

I had no problems just registering the CompanyName in my country. There was no other companies using any other variation of the name I chose though, so I didn't have to worry about differentiating/separating myself from anyone else. If your CompanyName is unique and not like anything else registered, you'd probably be fine to do the same.