Shallan Davar, Kholin, or Kholin-Davar?

[Usseewa]

What's her last name as of her marriage with Adolin?

[Returned he/him]

It's Kholin, though previously it was stated that she kept it as Davar:

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Jofwu

Did Shallan change her last name when she got married?

Brandon Sanderson

You do not change your last names if you are...

Jofwu

In Jah Keved?

Brandon Sanderson

Yes, so she did not change her last name. She is still Shallan Davar.

And there's also some... there's some weirdness there in line of succession stuff as well, which wouldn't be the case if she had been from Alethkar, and of certain, proper, you know... But the fact that she is not, she would keep her original name and would not be in succession for the throne.

Footnote: In Wind and Truth, it is revealed that Shallan did change her last name and was part of the line of succession.
JordanCon 2021 (July 16, 2021)

 

That's how it worked for Navani and Ialai, so presumably the same reasoning plays out for Shallan. Her role in the princedom make it more important to associate her with the ruling family than her previous one, not unlike Amaram taking the name Sadeas when he was elevated in Oathbringer.