The title being the character's name has always struck me as a direct, unsettling challenge. It's like Shakespeare is forcing you to ask: what exactly is Hamlet? The play isn't called 'The Tragedy of the Prince of Denmark' or 'The Revenge at Elsinore.' It's just 'Hamlet.' Every other character filters through his perception; we're trapped inside his head as much as they are. Polonius sees a lovesick youth, Gertrude sees a melancholy son, the ghost sees a tool for vengeance. The play circles this central question of his fractured self, and the title throws that question at you before you even start reading. It primes you to look for him, specifically, not just the plot. The soliloquies are basically him trying to answer the title.
A friend argued it's just a standard practice for tragedies, but I think that misses the deliberate claustrophobia of it. In 'Macbeth' or 'Othello,' the title still feels like it names the story, the subject. With 'Hamlet,' it feels like you're being introduced to a person, a consciousness you have to decipher, and the whole thing is an autopsy of that person's identity under impossible pressure. Even his famous inaction is a part of that identity puzzle. By the end, you still can't pin him down, which is kind of the point the title makes.