In Star Trek Into Darkness, the fugitive called John Harrison is actually Khan.
John Harrison is presented at first as a rogue Starfleet officer responsible for terrorist attacks. Captain James T. Kirk is ordered to pursue him to the Klingon homeworld, but the story later reveals that Harrison is Khan Noonien Singh, a genetically engineered human from Earth's past.
This version of Khan is portrayed by Benedict Cumberbatch and belongs to the alternate timeline created by Star Trek (2009). He is connected to Admiral Marcus and Section 31, which awakens and exploits his genetically enhanced crew. The film reworks elements from Star Trek II: The Wrath of Khan without repeating its original plot exactly.
The name “John Harrison” is an alias rather than Khan's true identity. That reveal is one of the film's central twists, while Khan's history as a superhuman leader links the alternate-era story to the original television series and films. The answer is not Admiral Marcus, who is the officer manipulating Khan's situation.