Complex sentence: The regiment was titled 19th (Alexandra, Princess of Wales's Own) Hussars after Alexandra, Princess of Wales; in 1908, when she became Queen Consort, the name changed accordingly to 19th (Queen Alexandra's Own Royal) Hussars.
Split into simpler sentences: The regiment was titled 19th (Alexandra, Princess of Wales's Own) Hussars after Alexandra, Princess of Wales. In 1908, when Alexandra became Queen Consort, the name changed to 19th (Queen Alexandra's Own Royal) Hussars.