In Greek mythology, Laius, king of Thebes, consulted the oracles and was told that he would have a son.  This son was going to kill him.  Consequently, when his son was born, he had him taken into the wilderness and exposed  to the elements.  The name Oedipus means “swollen feet”.  In the past, it was believed that this was because when children were left out in the elements, their feet were pinned together so that they could not save themselves in any way.  However, modern scholars are skeptical of this interpretation and discount it.  A shepherd found Oedipus and took him to Corinth, where he was adopted and raised by King Polybus and his wife. 

When he was a young man, Oedipus visited Delphi, the place known for oracles.  He, also, was told that he would kill his father and marry his mother.  He refused to return to Corinth for fear that he may just do that.   On his travels toward Thebes, he runs into Laius, has a quarrel with him, and kills Laius; therefore fulfilling the first part of the oracle.  He then continues on to Thebes, where he learns that the king has died, and the city is being plagued by the Sphinx.  He answers the riddle of the Sphinx, and for a reward is given Queen Jocasta in marriage.  So the oracle was fulfilled.  He killed his father and married his mother.  Upon marrying her, he became king.  “Rex” means king. 

So his name means Oedipus the King. 

Oedipus Rex is a classic Greek epic, so it makes sense that his name would come from the Greek language.

According to Wikipedia, Oedipus means "swollen foot" and originated from the Greek word "Oidípous".  According to legend, when Oedipus was born, his parents sent him away to avoid a prophecy which said he would one day kill his father and marry his mother.  Before he was adopted, Oedipus sustained injuries to his feet and ankles, causing him to swell - thus his name.

Rex means "reigning king" which is proven when the prophecy sadly comes true when Oedipus does eventually kill his father and become king.