In all three films Diana has been in, she is never referred to as "Wonder Woman". Likewise, the alias isn't seen anywhere in print either. The closest it has come is the logo used in Lex Luthor's data, being two "W"s. Likewise, Bruce Wayne is only called "Batman" three times in the run of the DCEU. Once by Perry White, once by Barry Allen, and once by Aquaman.
^ McAvennie, Michael; Dolan, Hannah, ed. (2010). "1970s". DC Comics Year By Year A Visual Chronicle. Dorling Kindersley. p. 187. ISBN 978-0-7566-6742-9. The daughter of Batman and Catwoman from Earth-2 found a new home away from home in the pages of Wonder Woman's monthly title...a regular gig as the back-up feature to the Amazing Amazon's lead story. Handled by writer Paul Levitz and artist Joe Staton, the Huntress faced the villainy of the swamp creature Solomon Grundy.
With Artemis' help, Wonder Woman tracked Zola down to a subway station, where they found a lock of fox fur. Realizing that Zola was with Dionysus, they went to Providence, where Dionysus was currently located. They found Dionysus captured by Cassandra's minion, the Minotaur. When Cassandra's forces were about to depart to Olympus, Wonder Woman ambushed them and hung onto their plane. When the jet arrived to Olympus, the mountain was hit by a massive explosion.
The Diana Prince alias also played an important role after the events of Infinite Crisis. Wonder Woman was broadcast worldwide killing a villain named Maxwell Lord, as he was mind controlling Superman into killing Batman. When Wonder Woman caught him in her lasso, demanding to know how to stop Superman, Maxwell revealed that the only way to stop him was to kill Lord, so as a last resort Diana snapped his neck. To recover from the trauma of killing another person, the Amazon went into a self-imposed exile for one year. On her return to public life, Diana realized that her life as a full-time celebrity superhero and ambassador had kept her removed from humanity. Because of this she assumed the persona of Diana Prince and became an agent at the Department of Metahuman Affairs. During a later battle with the witch Circe, a spell was placed on Diana leaving her powerless when not in the guise of Wonder Woman.