When all the problems have been solved, what problem did Algernon have that wasn't solved at the end of the play? Do you think it was important?

In this play, "The Importance of Being Earnest", at first, both polite and beatiful girls, Gwendolen and Cecily, love the name Ernest. They think that it has it's own music, that it is perfect and so earnest , and also, that it inspires absolutly confidance, so, the women dream with finding a husband called Ernest. During the play, both find a man called Ernest and they are engaged with them, although their real name isn't that, the men pretend to be Ernest because if they weren't Ernest things would change with their future wifes. Later, after many problems, the girls realize that Ernest doesn't exist and the boys tell the true to them. Finally, with the help of Miss Prism, and, after some discussions, Mr Worthing finds in the army list that his real name is Ernest. As a consequence of that, for Jack all the trouble that during the play he have had, have been solved ,so, Gwendolen, Jack's future wife thinks that he was destinated to get marry with a man called Ernest, and the couple is very happy.

But the case of Algernon is different his problem is not solved, he is not called Ernest. He said that he doesn't think that a christening would be the practical value for him when Lady Bracknell didn't consent to Gwendolen to get marry with Mr Worthing, so he really don't want call Ernest. That is why he is not going to be christened as Ernest.

In conclusion of all the acts that happened, I think that for him is not very important to not call Ernest in the end of the story. One reason is that he really doesn't want and the second one because Cecily accepts his real name. In the past, he knew that Cecily adored the name Ernest, so, he wanted to change the name for Cecily, now, that Cecily loves to much Algernon, she accept him with his real name, Algernon. Finally, Cecily and Algernon are happy also. That is why I don't think that in the future it will be a problem for the relationship of the couple.

Someone can tell me his/her answer or his/her opinion about my opinion?