They are a sponsor just not overall naming rights...
Just Google "Delta Atlanta Falcons" and this is the first link that comes up...
Delta teams up with Atlanta Falcons, Atlanta United and Mercedes-Benz Stadium | Delta News Hub
Continuing to deepen its ties to Atlanta, Delta will serve as the Official Airline of the Atlanta Falcons, Atlanta United and Mercedes-Benz Stadium, the new home of the Falcons and Atlanta United, for the next five years through the 2021 season...
....As a part of the agreement with Mercedes-Benz Stadium, the South Champions Club in the new stadium has been named the Delta Sky360˚ Club. The 25,000-square foot club is located on the field level and will allow club patrons constant access to the field throughout the game. The club is on the away sideline for Falcons games and the home sideline for all Atlanta United matches...
...In addition, significant elements of the partnerships include in-stadium LED advertising and IPTV exposure, as well as unique digital and social content opportunities.