This question clearly refers to another famous quote in this play, but one that was delivered to another character: Laertes. Let us remember that in Act I scene 3 Polonius gives his son the following advice as he returns to his studies:
This above all: to thine ownself be true,
And it must follow, as the night the day,
Thou canst not then be false to any man.
Given the fact that Laertes and Hamlet are foils for each other in the play, it is therefore important to ask ourselves if Hamlet is a character who is true to himself.
To be honest, I think this depends a lot on perspective. You could argue that he is true to himself, because rather than rush on and revenge his father's death, he is true to his naturally cautious nature and therefore, as a result, is very careful to make sure he has proof of the guilt of Claudius before he does anything about it. In this sense, we could definitely say that Hamlet is a character who is true to his own instincts.
However, I also think that it would be possible to argue that the way in which Hamlet prevaricates and procratinates indicates that he is not in fact true to himself at all. He seems to use procrastination as a barrier to action, and berates himself harshly at various points in the play because of this, therefore indicating that he does not think he is true to himself.
Either way, I think that in the final Act, we do see a picture of Hamlet who is being presented as at peace with himself and who has finally reached a stage where he is true to who he is.