Alice was checking up on a pregnant Amy in the infirmary, and she later left. ("LaFleur") A couple of days later, Alice walked past Pierre Chang, when he was going to the filming location to film the Arrow Orientation film. ("Because You Left") Alice was also seen in several Dharma background scenes, often with young children, presumably hers. When Pierre Chang organised the evacuation of all the DHARMA women and children from the Island, Alice was seen on the pier boarding the submarine with Sawyer and Juliet. ("Follow the Leader")
The actress who portrayed Alice also portrayed another DHARMA member, Fern.
Although both Fern and Alice were portrayed by the same actress, their hair had a little bit different.
Alice's name was supposed to come from her jumpsuit, which seen in "LaFleur", but it's too far to see, and hardly to identify her name. Thus, the actress had given some information about the name on her jumpsuit.
Alice was named after the actress who portrayed her.