What are some incidents and comments in the play that support the central theme of being true to one's self?
The entire plot of the play would be non-existent if Jack/Ernest knew who he truly was. All of the lies and deceptions come from the men pretending to be other people: Jack pretending to be Ernest to please Gwendolen, and Algernon pretneding to be Ernest in order to see Cecily. However, these women wouldn't have wanted anything to do with Jack or Algernon had the men not pretended their name was Ernest. Imagine if the deception had not unfolded and both men had gotten christened as Ernest and then married Gwendolen and Cecily. They would have had to live a lie, putting away any thoughts or associations with the former lives.
Gwendolen and Cecily, in a way, stay true to themselves in that they have both made a decision to marry a man named Ernest and are determined to do so. While this may seem petty, they stick to what they believe in.
Wilde is commenting that if Jack is Jack--Gwendolen is in love with him, no matter what his name is--but Wilde believes the higher society is so ridiculous that she would refuse to marry him based on a name (rather than income, land owned, the way he treated he, looks, etc).