Yep, you guessed it. Henry V is all about the famous English monarch... King Henry V.
Brain Snack: The first time the play was printed (in the first quarto of 1600), the publishers got fancy and gave it a really long title:
The chronicle history of Henry the fifth, with his battle fought at Agincourt in France. Together with Ancient Pistol. As it hath been sundry times played by the Right Honorable the Lord Chamberlain his servants.