Both Jack and Algernon want to be christened as Ernest because it is a convenient way for them to continue their double lives and maintain their respective personas. By being christened as Ernest, they can continue their relationships with Gwendolen and Cecily under the false pretense that they are both named Ernest. In addition, being christened as Ernest gives them a sort of freedom to separate their public and private personas, allowing them to indulge in their double lives without fear of being discovered.
