In 'Aliens', the little girl rescued by Ripley is Newt.
Newt's full name is Rebecca Jorden, and she is the only surviving colonist from Hadley's Hope on LV-426. The colony's residents were exposed to the alien species after investigating the derelict spacecraft first seen in 'Alien'. Newt survives by hiding in the colony's ventilation system, where the Colonial Marines eventually find her.
Newt becomes especially important because Ripley develops a protective, almost parental bond with her. During the escape from Hadley's Hope, the aliens abduct Newt and take her to their hive. Ripley refuses to leave her behind and descends into the processing station alone, eventually finding Newt near the alien queen and carrying her to safety.
A common mix-up is calling the child 'Rebecca', but that is her given name; 'Newt' is the nickname by which she is known throughout the film. The character was played by Carrie Henn, who later reprised the role only through archival material because Newt does not survive the opening of 'Alien 3'.