Parents who like Ben and Benjamin but find those forms too popular sometimes consider Benedict as a more distinctive choice. Unlike the Old Testament Benjamin, Benedict is the name of the saint who formed the Benedictine Order and of fifteen popes,including a recent one.
Shakespeare used a variant form--Benedick--for the character in Much Ado About Nothing. Other options are Bennett and Benno.
Benedict Cumberbatch is a rising British stage, film and TV actor, who has been seen as Stephen Hawking, William Pitt, Dr. Frankenstein, Frankenstein's monster, and currently as Sherlock Holmes in the BBC series.
Just one caveat: There is the link to that infamous traitor Benedict Arnold.