I think the key is to look at what the stadium is called at its first mention in the article text (because, yes, headlines and subsequent mentions in an article commonly use a shortened form).
- (the) Bernabéu: BBC, The Sunday Guardian, The Times, BBC
- Bernabéu stadium: ESPN, BBC
- Bernabéu Stadium: New York Times, Reuters, Sky Sports
- (the) Santiago Bernabéu: ESPN, ESPN, Sports Illustrated, New York Times, New York Times
- Santiago Bernabéu stadium: New York Times, New York Times
- (the) Santiago Bernabéu Stadium: Sports Business Journal, CBS News, Reuters, Reuters, Atlanta Business Chronicle
- Wembley Stadium: BBC, Rolling Stone, ESPN, BBC, Sports Illustrated, Billboard, The Sun
- Wembley: New York Times, Reuters, New York Times, Sport Illustrated, BBC, BBC, BBC, New York Times, BBC, Sky Sports, The Guardian
–−–−–−–−