Real Madrid does not win any matches and titles because of the big name and history of the club, but it is because of the strategy of the coach and the quality of the players. If they won it all because of the club's big name and history, then Milan and Manchester United should always be able to dominate the Premier League, Serie A and Champions League because of their name.
Exactly. Real Madrid could win some UCL trophies because they had good coaches who applied great tactics/strategies and they had quality players in their squad, too. Real Madrid couldn't win any title if they only rely on their big name. 
Real Madrid is a big team with good squad depth. Look and compare with the squad depth of other teams so you have to say one fact that Real Madrid did that because of the coach and the squad.
It was, you can state it when Real Madrid still had Ronaldo.