In The Terminator, the human resistance leader whose mother is targeted is John Connor.
John Connor is not yet born during most of the film’s events, but the future machine war makes him the target of the Terminator. A reprogrammed soldier, Kyle Reese, travels from 2029 to 1984 to protect John’s mother, Sarah Connor, before her son’s birth.
The film’s central time-travel premise explains why Sarah is hunted even though John is absent from the present-day action. In the future, John becomes the leader of the human resistance against Skynet, making his survival crucial to the resistance’s eventual struggle.
John later appears as a child in Terminator 2: Judgment Day, where he is protected by a reprogrammed T-800. This makes him distinct from Kyle Reese, the human soldier sent back to defend Sarah, and from Miles Dyson, the engineer linked to Skynet’s development.