Why was it important for Jack to know if he had been christened?

Miss Prism tells to all of them the true story about the male baby that she left in Victorian Station. As a consequence of that, and, after finding in the army list, Mr Worthing realizes that his brother is Algernon and his aunt Lady Bracknell. After, Lady Bracknell tells to him that he has already been christened, so, he already has a name, put by his real parents.

Maybe,if he hadn't have a name, he would change to Ernest and like this, he would have the name that Gwendolen dreams. In conclusion, for him is very important to know if he has been christened because, like this, he can know if he already has a name, and knowing this and depending the reply, he can decide his own name or to accept he isn't called Ernest.

Another answer? Can this be?