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.
Wonder Woman’s powers are a result of the blessings she received from the gods (or presumably in the modern version by her divine ancestry), but originally came from her "brain energy" training. Her abilities in large part come from her upbringing in the martial society of the Amazons. She is one of the most powerful superheroes in the DC universe.
“Closeup, full length figure of WW. Do some careful chaining here—Mars’s men are experts! Put a metal collar on WW with a chain running off from the panel, as though she were chained in the line of prisoners. Have her hands clasped together at her breast with double bands on her wrists, her Amazon bracelets and another set. Between these runs a short chain, about the length of a handcuff chain—this is what compels her to clasp her hands together. Then put another, heavier, larger chain between her wrist bands which hangs in a long loop to just above her knees. At her ankles show a pair of arms and hands, coming from out of the panel, clasping about her ankles. This whole panel will lose its point and spoil the story unless these chains are drawn exactly as described here.”
A shocked Diana apologized to Antiope and abruptly left the training session. She wandered off to a cliff on the Themysciran seashore and examined her gauntlets in awe. As she stood there, she noticed an airplane burst through the forcefield surrounding Themyscira and crash in the nearby waters. Seeing even from a great distance away that someone was trapped inside the sinking aircraft, she leaped down the ocean and rescued the pilot, none other than a human soldier named Steve Trevor. She pulled him out of the water and onto the Themysciran shore. As he came to, she noted in disbelief that he was a man, as she had never seen one before. Though somewhat confused, Steve affirmed that he was, rhetorically asking whether or not he looked like one.
Hermes attacked Wonder Woman there, refusing to simply give up the child, but during their battle, War ripped the baby from Demeter's womb and disappeared. Unable to let a grave wound such as that go unattended, Diana saw to Demeter first, and the goddess warned that War could not be trusted. Worriedly, Diana and Orion returned to Manhattan to find that War had returned the baby to Zola. At last, the baby and his mother were reunited - and Orion would not have to look any further for the child he needed to kill.