You might want to consider the way in which Wilde critiques Victorian society through the use of the name "Earnest." Really, the play is all about the importance of not being Earnest. Earnest of course denotes many aspects, including boringness, a sense of duty, pomposity and complacenty. All of these were identified by Wilde as characterising Victorian society. The play turns such distinctions on their head by using the word "serious" instead of "trivial" and vice versa. Thus it is that Algernon argues that those who are not "serious" about their food are actually "shallow," and Gwendolen champions style over sincerity in "matters of great importance."
Earnest then in the play relates to false truth and false morality. Note the way in which both Algernon and Jack have to create other selves to be able to escape the restrictions of Victorian society. There is also a central paradox in the play, as being earnest is shown to not necessarily be enough. Note the way in which the characters who embrace triviality and flout social norms are the ones who stand the most chance of gaining seriousness and morality. It does not pay to be Earnest!