Spoiler alerts for who lives and dies in Shakespeare plays. If you don't know who lives and dies in Shakespeare plays, then go see the plays right away and DON'T read the plot synopsis first -- they're a lot more fun if you don't know what's going to happen first. But, anyway.
First: if the title is who you are but not your name, you've got pretty good odds. The merchant of Venice, both merry wives of Winsor, the shrew, and both gentlemen of Verona survive. Only one of the two noble kinsmen survives, but that was a collaboration with another author, so if we say that the surviving noble kinsman is Shakespeare's and the dead one is Fletcher's.... Even if we don't, the odds of surviving if the title of the play refers to you but doesn't name you are a respectable 7/8, or 87.5%
Now, let's look at the characters whose names ARE the titles of their plays. The first thing we have to think about are the two-part and three-part plays. Do we say that Henry IV survived part one and died in part two, or do we just say that Henry IV died in "Henry IV", which was shown in two parts? I'm going to count "Henry IV Parts 1 and 2" to be one work for counting these, and "Henry VI Parts 1, 2, and 3" to be one.
Then we have to ask about Henry V. He doesn't die on stage, but his death is mentioned in the epilogue to the play. So I'd count that one as him not surviving the play.
So, for the History plays, we've got, in the "dead" category, King John, Richard II, Henry IV, Henry V, Henry VI, and Richard III. In "alive", we've got Henry VIII.
Antony and Cleopatra both die. Coriolanus, Hamlet, Julius Caesar, King Lear, Macbeth, and Othello all die. Romeo and Juliet, Timon of Athens, and Titus Andronicus all die. On the other hand, Cymbeline, Pericles, and both Troilus and Cressida survive.
So that's eighteen dead and five alive. If your title is the name of the play, you've got five chances out of twenty three to survive, or about a 22% survival rate if your actual NAME is the title of the play.
Putting it all together, we've got 19 dead and 12 alive, so your total odds are 12 out of 31, or about 39%.