Sometimes he's Henry. Sometimes it's Henri. At least once it's Aimerick. Just so you know, that's not me being sloppy. That's just the way names went back when. F'rinstance, William Marshall, Henry II's righthand man, was Guillaume le Maréchal on the south side of the English Channel. And in diplomatic missives and official seals, King John was Johannes Rex Anglorum.
And while we're on the subject, it was often more usual to celebrate your "name day" - the day dedicated to the patron saint after whom you were named - than it was to celebrate your birthday.