If DC/WB/New Line were smart, they would go all out and declare war over the "Captain Marvel" name. With the Shazam! movie announced before anything relating to Marvel's fake Captain Marvel, and Dwayne Johnson signed to star as the villain Black Adam, DC can easily take ownership of the name "Captain Marvel" in the public square by issuing press statements and news items all emphasising a phrase like "DC Comics' superhero Captain Marvel", which would then be picked up and repeated by news and press services ad infinitum.
And, I suppose, Disney-Marvel would want to fight it. In the words of Dwayne Johnson, "Bring it!" Any publicity is good publicity. But I honestly doubt they would want to fight it. For 40 years Marvel had no real problem with DC's Captain Marvel, except for the fact they obviously didn't want DC to publish a comic book with the title Captain Marvel. And DC was cool with that, naming the series Shazam!, after the wizard and the magic word that gave Captain Marvel his powers.
"But, Marvel recently won full use of the name Captain Marvel." That's the one I'm hearing a lot. But no one has come up with evidence of this supposed court case that gave Marvel Comics full ownership of the name Captain Marvel. Probably because you can't own a name. Just ask the Avengers. No, not the Marvel group... the British spies who also were created before their Marvel counterparts. Besides, DC still uses the name Captain Marvel in Justice League Beyond and the upcoming Thunderworld. So that argument is obviously an urban myth.
The real reason for the name change is that the new powers-that-be at DC have kind of gotten lazy. "Well, everyone already calls him Shazam anyway". So, then by that reasoning, JJ Abrams should change Captain Kirk's name to Star Trek, since... you know, people are dumb, and they'll think that's his name anyway. Or Disney should change Luke Skywalker's name to Star Wars. But thankfully the movie isn't exclusively DC. Warner Brothers and New Line Cinema are involved. I have confidence in them that they would want to embrace the character's history, and keep the traditional name. Superman's current costume has nothing in common with the New 52, except for the lack of trunks. There is no turtleneck or bulky kryptonian armor with red piping. In fact, the emblem is a complete throw back to the golden age. Ben Affleck's Batman costume. Is it New 52? No... it's a 30 year old Frank Miller design. Wonder Woman? No, no New 52 there... just some Xena in patriotic colors (washed out, of course). So I am confident not only will Captain Marvel be wearing some sort of costumed based on the traditional one and not the hoodie-obsessed New 52, but he will have his traditional name. Depending on who the director will be, it may become very apparent very quickly.
As I said, any publicity is good publicity, and if Disney really were to cause a controversy over this, it would only benefit the public consciousness of the Shazam! movie. So, come on and say the name: Captain Marvel.
Take it away, comics legend Neal Adams...