All of their names were given in a radio report on the first episode.
Natalie Shaefer really was pretty old when the show was on. She was pretty spry for her age.
The only character whose full name was never given on the show was Gilligan. Producer Sherwood Schwartz once said in an interview that, should there be a need for him to have a first name in one of the episodes, it would have been "Willie."