Rather prominently, Pike's first officer called herself "Number One" when asked in an official capacity. While she gets way more screen time in ST:Discovery, we never see her named. It's now apparently a gimmick of the series.
Was she ever given a name anywhere?
From the interview with the ST:DIS co-executive producer:
TREKCORE: Rebecca Romijn’s Number One went by ‘Commander’ or simply ‘Number One’ for most of her time on-screen, but it sounded like Pike did call her ‘Una’ one time during the finale — the character’s name from the Star Trek tie-in novels. It wasn’t in the captions, so can you confirm we heard that correctly?
PARADISE: Oh yes, it was Una.
This is how Captain Pike called her in Star Trek Discovery Season 2 Finale.
Therefore, it seems that the name shown on Netflix is a transcript error of her real and intended name 'Una'.
Here is what Memory Alpha has to say about her name. The upshot is there has never been a definitive canonical name assigned to her character, but she has been given a long string of possible names in various apocryphal works.
In the Marvel Star Trek: Early Voyages comic book series, this character was named Lieutenant Commander Robbins. Her first name was interrupted by other dialogue, but starts with "Eure—."
The novel Vulcan's Glory, by Star Trek: The Original Series writer D.C. Fontana, suggested this character's moniker was not simply a nickname or title — she was an Illyrian who was called "Number One," as the best intellect among her generation. The novels The Children of Kings and Child of Two Worlds explain that Number One does have a given name, but it's difficult to pronounce for non-Illyrians; the former suggests that she liked to be called by this name rather than her own as it enabled her to maintain a professional relationship with her captain. In the novel Captain to Captain she is referred to as "Una", however this is not her real name either.
In the Captain's Table novel Where Sea Meets Sky, Number One was given the last name "Lefler" (an allusion to Robin Lefler).
Star Trek II: Biographies gives her real name as Leigh Hudec.
Peter David's New Frontier series of novels had a character named "Morgan Primus" who was an immortal like Flint (from TOS: "Requiem for Methuselah") and was the mother of Robin Lefler. It is hinted that she and Number One are the same person.
...
In the Star Trek: Discovery novel, Desperate Hours, Number One had been promoted to Commander and was given the last name "Una".
There is no short answer to this question, here is a full account of what is known within the Star Trek universe about the Illyrian-born human Starfleet officer:
The name of the Star Trek character seen in Star Trek:Discovery as well as Star Trek: The Original Series has long been controversial however in Star Trek: Short Takes episode Q&A her official name is displayed on her PADD confirming that her official Starfleet name is Una during the time when she served as Captain Pike's First Officer.
In this same episode however she told Spock that
My name is Number One.
These statements are not necessarily contradictory:
Una is a girl's name in the English language derived from the Gaelic word for "unique." In many languages the word itself means "one":
Una is the Latin feminine word for numeral "1" (literally, it means "the number 1.")
Una is the Spanish feminine singular of the adjective uno = "One"
Une is the French feminine singular of the adjective un, and it is pronounced OO-na"
Una means "One" in Irish.
Long-time Star Trek writer Dorothy Catherine "D. C." Fontana explained the origins of this name in her novel Vulcan's Glory, which states that this character's moniker was not simply a nickname or title – she was a product of Illyrian genetic engineering who was called "Number One," as the best product of her batch.
As such, the name "Number One" is a literal English translation of "Una" so both statements are technically correct.
LCDR Una's rank and title:
At various times onboard Enterprise she is adressed as simply "Lieutenant" rather than "Number One" or "Lieutenant Commander." This is common the in Naval forces which Star Trek rank structure emulates. In the same way that "Captain" is both a billet title, which simply means it is your job to "captain" the vessel, or the same word is also a military rank; Lieutenant is both a position title and a rank. The military billet title 1st Lieutenant (abr. 1Lt) literally means that this person is the "First Officer" in succession of command, also known as the Executive Officer (XO), or "Number One," and occasionally just "Lieutenant." When the Captain addresses her as "Lieutenant" he is not using her rank, he is referring to her job. Her military rank aboard the Enterprise has always been Lieutenant Commander (LCDR) and as the script was written her job has always been to be the Executive Officer (The Making of Star Trek, pp. 22-30)
Given Name:
LCDR Una's given name on Illyria is impossible to pronounce according to some novels and it has not yet been revealed within a canonical source.
