Georgia O'Keeffe continued using the surname O'Keeffe after her 1924 marriage to Alfred Stieglitz.
O'Keeffe married Alfred Stieglitz in 1924, but she remained publicly and professionally known as Georgia O'Keeffe. Her established artistic identity did not become “Georgia Stieglitz,” and her works continued to be signed and catalogued under O'Keeffe.
Stieglitz was a major photographer, gallery owner, and promoter of modern art. He exhibited O'Keeffe's work and made hundreds of photographs of her, but their professional relationship should not be mistaken for a shared artistic name.
The apostrophe is part of the surname's standard spelling. O'Keeffe's name is also sometimes incorrectly written without the apostrophe or combined with Stieglitz; neither form is the canonical answer to this question.