Carol Danvers took up the mantle of Captain Marvel and made it her own, but technically she shouldn’t be referred to as a "captain" at all. Captain Marvel #1 reveals that the name "Captain Marvel" is actually inaccurate when it comes to Carol.
Carol Danvers was not the first hero to go by Captain Marvel in the Marvel Comics Universe. That honor belongs to Mar-Vell, a captain in the Kree Space Fleet. Mar-Vell infiltrated NASA by posing as a human scientist; there, he met Carol Danvers, the head of security at the time. Carol was eventually knocked into a Kree Psyche-Magnitron, which unlocked her latent powers. Initially, she operated alongside Mar-Vell as Ms. Marvel until Mar-Vell sacrificing his life inspired her to take up the mantle and honor his legacy by becoming Captain Marvel.
In 2012’s Captain Marvel #1, written by Kelly Sue Deconnick with art by Dexter Soy, Carol reveals that she really shouldn’t be called "captain" at all. The issue opens with the newly minted Captain Marvel teaming up with Captain America to take on Absorbing Man in New York City. Absorbing Man jabs at Steve Rogers for taking orders from a “broad,” but Carol quickly shoots back, “This ‘broad’ left the service a full bird colonel. So technically, I outrank him.” Steve then grumbles good-naturedly that he’s been trying to get Carol demoted for years, and even calls her “sir” a few panels later.
When it comes to legacy titles, in recent years Marvel has depicted the passing of the star-spangled torch from Steve Rogers to Sam Wilson, and DC Comics is currently exploring Jon Kent’s struggle to establish himself as the new Superman. The mantle of Captain Marvel isn’t as widely known as a legacy title, perhaps because the MCU completely bypassed Mar-Vell and chose for Carol to originate the title in film. However, the disparity between the name Captain Marvel and Carol’s higher ranking as colonel proves just how important honoring Mar-Vell’s legacy is to her, so much so that she would choose to effectively demote herself in the public eye.
It’s always fun to see Marvel’s two captains bickering with each other, and though Steve seems jokingly reluctant to call Carol "sir," he is also the one who later encourages her to take up the Captain Marvel mantle. The fact that she accepts it reveals both the poignant significance behind the name Captain Marvel and just how much Carol Danvers admires Mar-Vell.