If you can avoid it at all, ...
Do not change an established brand name!
One major factor in selling books are readers looking for more books by the same author. You do not usually want to lose those sales.
Successful authors who change their names usually do this precisely because they do not want the new name associated with the old. J. K. Rowling used a pseudonym for a fresh start in crime. Stephen King used a pseudonym not to flood the market (and to see how his writing would sell if it wasn't attached to his famous name). The most common reason for many writers to publish under different names is when they write in genres with incompatiple audiences and do not want readers of one genre (say, children's fiction) to follow them into the other (e.g., erotica).
Unsuccessful authors sometimes do change their names to break the connection to that "failure" and give their careers a fresh start. As Megan Lindholm has stated in interviews, she began using a pseudonym because her novels, published under her own name, didn't sell well and booksellers didn't order her books, further limiting her potential sales. So she began publishing as Robin Hobb and is now a bestelling author under that name.
Successful brands who have to change their name usually try to keep the connection. When the name of the popular chocolate bar "Raider" was changed to "Twix" in many European countries, an expensive marketing campaign was started to keep the buyers. The advertising slogan in Germany, for example, was "Raider is now called Twix, otherwise nothing changes" (the German sentence rhymes). You can often see the same intense ad campaigns when companies are bought or merge and brand names change.
A common practice when old brand names need to be kept is to create a new brand name that combines the old name with the new. When Daimler and Crysler merged, they called the new company Daimler Crysler. When musician John Cougar chose to use his real family name, he kept the pseudonym Cougar and called himself John Cougar Mellencamp for a while, until the new name had been established and he could drop the Cougar completely.
What I would advise in the case of a female author marrying and changing her maiden name is to:
Change the legal name but keep publishing under the maiden name.
There is no reason why an author's brand name must match their legal name.
As a second option, the author could change the brand name to a combination of their maiden and their new familiy name creating a double name in the way John Cougar Mellencamp did. I find this option potentially confusing for readers and the resulting names usually unattractive and awkward.
The best approach, in my opinion, is to stop thinking of the name on your books as "your name" and to begin seeing it as a brand name, and treat it as such.