Successful/ known under both maiden and married name.

[denquixote]

Clare Booth Luce was a well known writer who married the editor of Time Magazine. As Clare Booth she wrote "The Women" and other plays and books as well as political essays. As Clare Booth Luce she campaigned for every Republican candidate from Eisenhower to her death ands served as Ambassador to Italy among other posts.

[Annie-Xmas]

Christie Perfect was well known as a member of Sugar Shack before she married John McVie, and became Christie McVie, which led to supergroup Fleetwood Mac

[the_diego]

Linda Day George
Sharon Marie Tate Polanski
Farrah Fawcett Majors

[Beware of Doug]

Harriet Nelson first gained fame as Harriet Hilliard, singer with Ozzie Nelson's band. They actually worked together for several years before their marriage.

[Kimstu]

Mary I of England was pretty renowned both before and after her marriage to Philip of Spain, although of course surnames as such were not such a big issue for her.

[Kimstu]

Also, the popular journalist Nellie Bly (the pen name of Elizabeth Jane Cochrane) became the noted industrialist and inventor Elizabeth Cochrane Seaman in her widowhood, before going back into journalism after her company's bankruptcy. Not sure if she counts as literally known under her "maiden" name, since the name in question was a pen name.