The ESV is typical in it's rendering of Barabbas' name:
Now at the feast the governor was accustomed to release for the crowd any one prisoner whom they wanted. And they had then a notorious prisoner called Barabbas. So when they had gathered, Pilate said to them, “Whom do you want me to release for you: Barabbas, or Jesus who is called Christ?” For he knew that it was out of envy that they had delivered him up. Besides, while he was sitting on the judgment seat, his wife sent word to him, “Have nothing to do with that righteous man, for I have suffered much because of him today in a dream.” Now the chief priests and the elders persuaded the crowd to ask for Barabbas and destroy Jesus. The governor again said to them, “Which of the two do you want me to release for you?” And they said, “Barabbas.” Pilate said to them, “Then what shall I do with Jesus who is called Christ?” They all said, “Let him be crucified!” And he said, “Why, what evil has he done?” But they shouted all the more, “Let him be crucified!”—Matthew 27:15-23 (ESV)
The NRSV translation, however, says that his name is Jesus Barabbas:
At that time they had a notorious prisoner, called Jesus* Barabbas. So after they had gathered, Pilate said to them, ‘Whom do you want me to release for you, Jesus* Barabbas or Jesus who is called the Messiah?’—Matthew 27:16-17 (NRSV)
The footnote reads:
Other ancient authorities lack Jesus
So was his name Barabbas or Jesus Barabbas?