Henry m. Old High German heim, Old Frankish *haim 'home' + Old High German rih 'ruler'.
The name of a 10th C king of Germany, an 11th C king of the Franks, an 11th C Holy Roman emperor and saint, two other 11th C Holy Roman emperors, two 12th C Holy Roman emperors, two 12th C kings of England, a 13th C emperor of Constantinople, a 12th C king of the Slavs, a 13th C high duke of Poland, a 13th C king of Navarre, a 13th C king of Castile, a 13th C king of England, a 14th C king of Castile, a 14th C king of Germany and Holy Roman emperor, a 15th C king of Castile, three 15th C kings of England, a 15th-16th C king of England, a 16th C king of Portugal, a 16th C king of Navarre, two 16th C kings of France, a 16th C king of France and Navarre, a 16th C king of England, as well as numerous saints.
The English diminutive Hen and the vernacular Henri are witnessed in 1379 in the relational bynames Hensoñ (WRYPT1 p. 15) and Henrivif' (WRYPT1 p. 43).