People also have nicknames or variations of their name they actually use. Like with her it could be Mikah or something(which is not uncommon with female versions of the name Michael).
Also, I think its a mistake to base a show in a single person. It's only natural to base it on a group of people and in time I'm sure this is going to happen cause there is simply no other way to do it in a satisfactory way. Saru, Lorca, Landry, Nambue, Burnham will all interact alot whether or not it's through Burnham's perspective. And they will factor in greatly for the success of the story.
Also imo, progressivelly we will just have to see plot points were Burnham is not seen at all, cause this will be the need of the story(e.g. crewmember that has to infiltrate an alien installation while Burnham is doing something else) Even when the Captains were on the focus, this naturally happened before. And for a succesful series, it shouldn't really matter or be an issue that it happens.