The correct signature for Mrs. Jones is Mary Jones or Mary Smith Jones. Then under her signature she writes in parentheses, "Mrs. John Henry Jones." An unmarried woman puts "Miss" in parentheses at the left of her signature.
If you sign your name "Mary Smith Jones" and close under it you write clearly "Mrs. John Henry Jones," it should be obvious that "Mrs. John Henry Jones" is the way you are to be written to, and "Mrs. Jones" is the way you are to be spoken to.
One other detail that I want to underscore because it is so important: Correctly, a widow always continues to use her husband's name. He did not lend it to her; he gave it to her, and she keeps it all her life or until she marries again.
A wife's visiting cards should be engraved with her husband's full name: "Mrs. John Henry Jones," but if he prefers to call himself, "J. Henry Jones" or "John H. Jones," his wife's card should match his. EMILY POST, in a Radio Talk.