I'm calling it now, I reckon the reason we have a well known actress playing number one is because she will be discovery's captain for season 3.
I really don't understand the "mystery" surrounding Number One's name. That was solved in 1987 with the creation of Will Riker. The only reason we never learned her name is because the character did not continue beyond 1965. If Star Trek had gone into production with The Cage's cast, it's possible, unlikely given 1960's TV production practices, but possible, that we would have heard her name at some point when the series was on NBC.
As far as "getting the character right"... considering that Majel Barrett in 1964 hadn't yet developed the acting chops that she displayed later in her career, and arguably wasn't quite up to the task of carrying this role, I'm hoping that this new depiction of Number One will be better and more compelling than how the character was originally presented in "The Cage." Kor
It is impossible for them to "get things right" as expectations will vary form individual to individual.
Yeah, the reason the character was dropped was because the network executives didn't like MB as an actor, and wanted it recast. I am sure RR will be up to the task.
Also, this might be an unpopular opinion but Majel Barrett was...an actress of limited range at the time. It's well known that she only had the role in the pilot (along with her later, more circumscribed role as Nurse Chapel) because she was "dating" Gene. As time wore on, I think Majel's range improved. I actually love some of the performances she did as Lwaxana Troi, like Half a Life, Cost of Living, and Dark Page. But there is nothing aside from nostalgia which makes her role in The Cage all that spectacular. Edit: Oops, didn't see Kor basically said the same thing I did. I'll leave this here anyway.
This - by any objective standard we (canonically) know next to nothing about her, so there is less to get right than if they introduced Mordock the Benzite. But there will be people with a whole fleshed out personality and history in their heads which they are expecting to see replicated.
Of course, all the characters of "The Cage" have the same excuse for not quite being themselves. Pike is borderline suicidal because he has just botched a command job - and this carries consequences for the whole troupe. Spock is limping because of the beating he took, apparently as the result of Pike's error. Boyce has sewn shut a couple of body bags recently. Colt is trying to fill in for a dead lad who apparently was close to the Captain, and getting bad feedback for no reason of her own. Certainly our Number One is entitled to a degree of shell shock, too, if it ever comes to that. Timo Saloniemi
... if They don't... There'll be a lot of Number 2 being tossed around here. Might I suggest that everybody hide your fans?
Except that those materials are not really consistent with each other. We've basically had fifty years of different people extrapolating from her brief appearance in "The Cage," but none of that is remotely definitive, including my own books.
In her spare time she overloads phasers and waits with a stopwatch for Pike to throw himself on them.
There are certainly some on-screen cues from The Cage that could be followed and expanded upon, but I don't think it is necessary to follow any "non on-screen" intentions that the production team may have had back in 1965. For any TV show, and just about any TV character, there are often things that get discussed in production meetings and written down about a certain character that never makes it to the screen -- and doesn't make it to the screen for intentional reasons. I guess I'm saying that even if Roddenberry wrote in his notes some aspects he had in mind for Number One, that doesn't mean that everything he wrote would have made it to the screen, even if The Cage had been picked up for production. That's why canon almost always (always?) is what was presented on screen, not what might be in production notes.