At the end of season 2 of "Stranger Things," Jim Hopper legally becomes Eleven's adoptive father. Hopper had secretly sheltered Eleven in a cabin while government agents searched for her, but their arrangement was tense because he restricted her movements to keep her safe.
Their relationship changes after Eleven helps Hopper close the gate beneath Hawkins National Laboratory. Hopper then makes a deal with Dr. Sam Owens to obtain official adoption papers, allowing Eleven to live openly under a new identity: Jane Hopper. The paperwork is shown in the season 2 finale, "The Gate," during the Snow Ball dance.
The answer is sometimes confused with Dr. Owens, because Owens helps arrange the legal protection and gives Hopper the documents. Owens, however, is not Eleven's adoptive parent. Joyce Byers is also an important parental figure, but Hopper is the person who legally adopts her. Hopper's adoption completes his movement from grieving, isolated police chief to a protective father figure.