The new manager is Rafael Benitez.
Rafael Benitez is the manager of Inter club in Italy.
No, it is just quicker to say Inter than Inter Milan.
Inter Milan are an Italian side.
Because Inter originated from Milan
Inter Milan plays in the Italian league (Serie A)
It was Inter Milan.
No Mr Greenhouse is not playing for Inter Milan.
No, Inter Milan or to give them their full name, Football Club Internazionale Milano are from Milan, Italy.