During the times when surnames first began to be used in this region, a common way to create a surname was to use the given name of the father. Such names are classed as patronymic surnames. Enrico was created from came from the Teutonic name Henry. In fact, the name Henry is derived from the Old German Haimric which means home-rule. There were many Teutonic names in Italy following the fall of the Roman Empire.
In comparison with other European surnames, Italian surnames have a surprising number of forms. They reflect the regional variations and the many dialects of the Italian language, each with its own distinctive features. For example, in Northern Italy the typical Italian surname suffix is "i", whereas in Southern Italy it is "o". Additionally, spelling changes frequently occurred because medieval scribes and church officials often spelled names as they sounded rather than according to any specific spelling rules. The spelling variations in the name Enrico include and others.
Roger Enrico (1944-2016), American businessman, CEO of PepsiCo (1996-2001), CEO DreamWorks Animation SKG Inc (2004-2012)
Francesco Enrico Speroni (b. 1946), Italian politician and Member of the European Parliament for the North-West Italy
Michele Enrico Carafa di Colobrano (1787-1872), Italian opera composer
Davide Enrico Somma (b. 1985), South African footballer
Marco Enrico Bossi (1861-1925), Italian organist, composer, improviser and pedagogue
Enrico Ferri (1942-2020), Italian politician and magistrate, Secretary of the Italian Democratic Socialist Party (1993-1995)
Mr. Enrico Fortunato Capaldi B.E.M., British recipient of the British Empire Medal on 8th June 2018, for services to charity and to the community on Teesside 
Enrico Alberto (1933-2019), Italian professional football player and manager
Enrico Castellani (1930-2017), Italian painter associated with the zero movement
Enrico A. Lazio (b. 1958), American Republican politician, U.S. Representative from New York 2nd District, 1993-2001; Delegate to Republican National Convention from New York, 1996; Candidate for U.S. Senator from New York, 2000