The Wachowski brothers, writers and directors of The Matrix films were fans of Neil Gaiman and based the character of Morpheus on the title character from the comic book The Sandman, also adopting one of his most common pseudonyms, Morpheus. They gave Fishburne some or all of the series to read, and the style of speech and mannerism of the Matrix character are heavily informed by the Sandman character, although since The Sandman is only a graphic novel, much of the tone and inflection is an original (though recognizable) interpretative creation on Fishburne's part. This connection is hinted at again in Enter the Matrix when Niobe calls Daniels Institute of dreams to get in touch with Morpheus.
There is also an oblique reference in Morpheus' name to the character of Orpheus in classical mythology. In Greek myth, Orpheus is known as the only living mortal to successfully visit the underworld and return alive; while the Matrix character Morpheus successfully travels between the "real world" and the world of the Matrix without penalty.