If you're approaching Shakespeare's exploration of the loss of identity solely with regard to the character of Hamlet, the questions to ask are: Does Hamlet experience a loss of identity in Shakespeare's Hamlet? If so, how is this loss of identity reflected in Hamlet's behavior? How does Hamlet's behavior affect other characters, and in what ways do they accommodate Hamlet's behavior?
One issue that you'll encounter right away in assessing whether Hamlet is experiencing a loss of identity is determining what Hamlet's character and personality were like before he first appears in the play.
What was Hamlet like before his father died, and before he returned to Denmark and to his family and court at Elsinore Castle?
There's no reliable frame of reference in the play itself to compare Hamlet's "former self" to his "current self." Horatio, Hamlet's college friend at Heidelberg, says very little about Hamlet's "former self," and Hamlet's childhood friends, Rosencrantz and Guildenstern, are at Elsinore at Claudius's behest to observe Hamlet's current, seemingly "distracted" behavior, not comment on their childhood play-dates together.
Nevertheless, characters like Claudius, Polonius, Gertrude, and Ophelia have noticed, and commented, that something is changed about Hamlet, but they seem to have differing opinions about what that "something" actually is, or what it means.
You can best approach this issue empirically, by observing Hamlet's current behavior and using what facts you know about him to come up with a plausible theory as to whether or not Hamlet suffers a loss of identity in the play.
The causes of loss of identity include major, traumatic, or otherwise significant events or changes in a person's life, including, for example, marriage and divorce, losing a loved one, relocating, and losing or getting a job.
Hamlet hasn't married anyone recently, but his mother has, and Hamlet seems pretty upset about it. Hamlet has lost a loved one, his father, and he might well be on the way to losing another loved one, Ophelia. Hamlet recently moved from a fairly calm and stable environment at college in Heidelberg to the turmoil and chaos of life at Elsinore. He's also lost what he assumed would be his job as King of Denmark to his uncle, Claudius. His uncle is the reason for his mother's re-marriage, and might also be the reason for his father's death.
Hamlet seems to have more than enough causes to get him started down the road to an identity crisis.
Loss of identity frequently manifests itself in physical and emotional behavior such as depression, mood swings, apparent feelings of hopelessness or worthlessness, suicidal thoughts, loss of interest in activities a person once enjoyed, irritability, and issues with concentration, energy levels, motivation, and sleep.
Does Hamlet demonstrate any of these kinds of behavior? Ask the characters around him.
Speaking of which, what have these other characters done to accommodate Hamlet's sometimes seemingly erratic behavior, mood swings, irritability, and other manifestations of a possible loss of identity? Polonius and Ophelia interact quite a lot with Hamlet, and his mother, Gertrude, also has a notable encounter with him. How did these characters maintain their own sense of self—if they actually do maintain it—in the midst of dealing with Hamlet's issues and behavior? What do these characters to either alleviate or worsen Hamlet's identity issues?
An extraordinary aspect of the characters in Shakespeare's plays is that we get to listen to their private, innermost thoughts, and hear them express their true feelings about themselves, other characters, and their particular circumstances. Through Hamlet's soliloquies, and through the soliloquies and "alone time" of a few other characters in the play, we can know exactly what Hamlet and these other characters are thinking and feeling about the people and events in their lives that most affect them and their behavior.
If Hamlet is experiencing a loss of identity, he might be talking to himself about who he really is, and questioning his role in society, his sense of self, his beliefs, his spirituality, his values, his relationships, or even his existence. He might be formulating a course of action to help himself regain his sense of identity and to help him reassert himself and regain his presumably rightful role in society. He might be searching for logic, reason, meaning, and passion that he believes are missing from his life.
At one time or another during the play, Hamlet talks to himself about each one of these things.
Your thesis statement should be based on the question of whether or not Hamlet experiences a loss of identity in Hamlet.
You main points should include specific references to the ways in which Shakespeare explores the causes, symptoms, and effects, if any, of Hamlet's loss of identity on himself an on other characters, or an explanation of why you don't think that Hamlet suffers from a loss of identity.
If you're approaching the loss of identity issue regarding the play as a whole, simply expand the same inquiry to include the other major characters, and compare the ways in which each characters manifests their loss of identity—if they have one—to the behavior of other characters.
Hamlet, for example, becomes indecisive, petulant, irritable, and withdrawn. Ophelia indiscriminately tosses flowers around the castle, goes crazy, and supposedly drowns herself in a brook. Claudius tries his best to be human, or even appear human, but he can't quite manage it. Gertrude is a seething mass of self-recrimination and self-loathing. Only Polonius seems entirely content with who and what he is, and he appears to give no thought to having any personal identity at all.