Why did Worthing try to convince Gwendolen that Jack was a good name?

The people who live in the country know about Mr Worthing like Jack, and Jack has got a wicked brother called Ernest in town. But really Ernest doesn't exit. Although people of town calle to Worthing Ernest.

Mr Worthing try to convice Gwendolen that Jack was a good name because his real name in the country in that moment is Jack, although people calle to him Ernest in town. So Gwendolen, a girl who lives in the town thinks that his name is Ernest. But, after telling about his name story to Algernon, he decide to be earnest to his future wife Gwendolen and to get rid of Ernest, so he try to convice that Jack is a good name. Can it be?