Connor Brennan is mentioned as the infant son of Tom Brennan, therefore his last name is presumed to also be Brennan. His mother's name is Rachel.
Connor was visiting his maternal grandparents in Cedar Rapids, Iowa, when his father was killed. He was 22 months old at the time. Connor has not been shown on Lost, except for being depicted in a photograph. ("Born to Run")
Lost-TV forum - "Picture People" thread, for characters seen in Lost only in photographs.