We don't know, at least not (yet) for sure. Biographer Schindler was the first who tried to identify the mysterious lady. His choice was Giulietta Guicciardi, the girl to whom Beethoven had dedicated the Moonlight sonata. Later on biographer Thayer's choice was Therese Brunswick, Giulietta's cousin. Biographer Frimmel's choice was Magdalene Willmann, Unger's choice Bettina Brentano, Marek's choice Dorothea Ertmann, et cetera, et cetera. It's not easy to mention the name of a female friend of Beethoven's who has NOT been put on the list of candidates! These days Solomon is by far the most fashionable Beethoven biographer in the UK and the USA and his choice is Antonie Brentano, Bettina's sister-in-law. However, in Europe most biographers prefer Josephine Brunswick, Therese's sister, put forward by La Mara in the twenties, again in the fifties by Kaznelson and finally in the seventies and eighties by Goldschmidt and Tellenbach, lately also by Steblin, whose research threw very exciting new light on the riddle. Another, highly unlikely candidate is Marie Erdody, suggested by Steichen in the fifties and by Altman in 1996. Lately three new candidates were added to the list: Almerie Esterhazy, put forward in October 2000, Barbara von Tschoffen, put forward in June 2002, and Maria Anna von Liechtenstein, put forward in late 2002. I give them little chance. Surprisingly in 2002 Walden did an heroic attempt to defend the candidacy of Bettina Brentano, already decades ago correctly (in my opinion) put aside. The latest news on the Immortal Beloved is Klapproth's devoted attempt to convince the world that Josephine was Beethoven's one and only beIoved. He may be right indeed. Josephine's chances are by far the best.
See:
Unger, Max. Auf Spuren von Beethovens "Unsterblicher Geliebten". (Langensalza, 1911).
La Mara (Marie Lipsius). Beethoven und die Brunsviks. Nach Familienpapieren aus Therese Brunsviks Nachlass. (Leipzig, 1920).
Kaznelson, Sigmund. Beethovens Ferne und Unsterbliche Geliebte. (Zurich, 1954).
Marek, George. Beethoven. Biography of a genius. (New York, 1969).
Solomon, Maynard. Beethoven. (London/New York, 1977).
Goldschmidt, Harry. Um die Unsterbliche Geliebte. (Leipzig, 1977).
Tellenbach, Marie-Elisabeth. Beethoven und seine 'Unsterbliche Geliebte' Josephine Brunswick. (Zurich, 1983).
Beahrs, Virginia. The Immortal Beloved Revisited. In: The Beethoven Journal (San Jose, 1986).
Brandenburg, Sieghard. Beethovens Brief an die Unsterbliche Geliebte. (Bonn, 1986).
Solomon, Maynard. Beethoven Essays. (London/New York, 1988).
Lund, Susan. Raptus. A Novel about Beethoven. With Introductory Articles. (Melbourn, U.K., 1995).
Altman, Gail. Beethoven. A Man of his Word. (Tallahassee, 1996).
Celeda, Jaroslav and O. Pulkert. The Immortal Beloved. In: The Beethoven Journal (San Jose, 2000).
Pulkert, Oldrich. Almerie Esterhazy Revisited. In: The Beethoven Journal (San Jose, 2002).
Brauneis, Walther. "...mache dass ich mit dir leben kann" Neue Hypothesen zur Identitat der 'Unsterblichen Geliebten'. In: Osterreichisches Musikzeitschrift (Wien, 2002).
Buschmann, Brigitte. Gibt es neue Erkentnisse zu Goldschmidts Buch 'Um die Unsterbliche Geliebte'? In: Kunstwerk und Biographie. Gedenkschrift fur Harry Goldschmidt (Berlin, 2002).
Steblin, Rita. "Auf diese Art met A geht alles zu Grunde". A new look at Beethoven's Diary Entry and the "Immortal Beloved". In: Bonner Beethoven-Studien. (Bonn, 2007).
Walden, Edward. Beethoven's Immortal Beloved. Solving the Mystery. (Landham, Maryland, USA, 2011)
Klapproth, John E. Beethoven's Only Beloved: Josephine! (Charleston, SC, USA, 2011)