What makes Algernon suspect Ernest's identity in Oscar Wilde's "The Importance of Being Earnest" is that he finds the cigarette case with his name on it. Algernon knows Jack as Ernest, even though his real name is Jack, which is something Algernon wasn't aware of until he found Jac'/Ernest's cigarette case. The case had an inscription on it, saying "from little Cecily to her dear uncle Jack." This, of course, made Algernon suspicious.