The name d’Onofrio literally means “son of Onofrio.” Onofrio is a male personal name. The name is derived from a 4th/5th century saint, San Onuphrius. According to the Dizionario dei Cognomi Italiani, by Emidio De Felice, this name comes from the Christian Latin Onnuphrius, an adaptation of the Egyptian epithet Onnophris (meaning "always happy") from the Egyptian god Osiride. The name was spread through Italy during the Crusades, with the worship of Saint Onofrio, hermit and martyr of Thebaid, Egypt.

San Onofre is the Spanish variation of the name.

More information on the saint can be found here:

http://saints.sqpn.com/sainto14.htm

Some artistic images of San Onofre found here:

http://usuarios.lycos.es/novenaasanonofre/IndexImagenes3.htm

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An interesting website (in Italian) provides information showing where current d’Onofrio families live in Italy. A map showing the clusters can be accessed with this link:

http://gens.labo.net/it/cognomi/genera.html?cognome=D%27ONOFRIO&t=cognomi

It is interesting to note that the major cluster resides in the Campania and Naples region. Additional smaller clusters in Pescara and Milan can be found. The name can be found throughout most of Italy, but is more prevelant in the south.

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Famous people with last names d’Onofrio or Donofrio:

Vincent d’Onofrio, American movie actor
Nicholas Donofrio, Executive Vice President of Innovation and Technology, IBM Corp.
Beverly d’Onofrio, Author, Riding in Cars with Boys
Heather Daly-Donofrio, Professional golfer

I believe this is a Russian variant of our name, though I am not certain:
Yuri Onufriyenko, Russian Cosmonaut