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.
Later, when the play was published in the first folio edition (1623), the publishers decided to keep it simple and called the play The Life of Henry V. Check it out for yourself.