Wow! What a clever question!
This question could be open to a discussion post given that the play is loaded with epigrams and puns, all geared to kind of laugh at being sincere, or having a virtuous life of honesty.
This being said, we would have to look into Algernon's lines, particularly in Act I, when he describes the need for leading a double life or, as he calls it, "Bunburying". This is a good act in which you can look for puns as well because Ernest discloses his double life as Jack/Ernest, to Algernon's delight.
Think about the following:
You have always told me it was Ernest. I have introduced you to every one as Ernest. You answer to the name of Ernest. You look as if your name was Ernest. You are the most earnest-looking person I ever saw in my life.
From that quote alone we could come up with:
- Looking like an Ernest.
-A most earnest- looking man.
Another place in the play where you can find good puns on honesty can be found between the dialogues between Jack and Lady Bracknell in Act III, after Prism discloses how she lost the baby she was supposed to care for (Jack/Ernest). Jack refers to Gwendolen, his fiancee, with the following quote:
Gwendolen, it is a terrible thing for a man to find out suddenly that all his life he has been speaking nothing but the truth. Can you forgive me?
To which she says: "My own Ernest" over and over throughout.
Hence, we can conclude that another good title from a pun would be that: My own Ernest.
Like I said before, there are so many puns in the play that maybe in a discussion post you may get even more great answers!