Yes, Carol Danvers, referred to as Vers by the Kree, is Captain Marvel and so is the titular character.
Marvel’s official website shows this:
Carol Danvers becomes one of the universe's most powerful heroes when Earth is caught in the middle of a galactic war between two alien races.
She is never referred to as Captain Marvel during the events of the film however.
Note that whilst it isn't explicit evidence Carol is first referred to as Captain Marvel on screen in the Spider-Man: Far From Home trailer.
Peter Parker: There’s got to be someone else you can use. What about Thor?
Nick Fury: Off world.
Peter Parker: Captain Marvel?
Maria Hill: Unavailable.
Spider-Man: Far From Home, Trailer 1
This changes slightly in the film and we get the following. Note that it is actually
Talos here and not Fury
though so that is why the dialogue is slightly different and the change makes sense.
Peter Parker: Sir, come on. There's gotta be someone else you can use. What about Thor?
Nick Fury: Off-world.
Peter Parker: Okay, umm... Doctor Strange?
Nick Fury: Unavailable.
Peter Parker: Captain Marvel!
Nick Fury: Don't invoke her name.
Spider-Man: Far From Home