Expedia, Booking.com and Kayak all display the airline logo and use the American Airlines trademarked name, seemingly without issue.

Advertising reduction for American Airlines advertising England. Crenellated castle towers and fortifications in white, black, and gold on red ground. In black text, upper center: AMERICAN AIRLINES; ...

Poster for American Airlines advertising New England. View of hilly countryside with a rock wall in the foreground, and a small chapel behind it tucked into the hillside. In black and white text, ...