I have only heard Cortana say "chief" That is all I Heard and I've tried looking it up, but I found nothing

2 Answers

Master Chief's real name is John. Nobody really knows his what his last name was as when we was "acquired" for the Spartan II program he was simply John-117.

You can read more about John's backstory by reading The Fall of Reach(a better choice) or by reading the Wiki here(a quicker choice)

His first name is John. His last name is unknown (he was abducted by ONI when he was 6). His designation in training was John-117, and throughout the Covenant War before the events of Reach he was just Spartan-117 or Master Chief.