Alexa Ray Joel is his daughter's name (the Ray for
Ray Charles, if I'm not mistaken). Likely the ship is named after his daughter to emphasize the fact that the
fishermen are indeed doing this and
sacrificing themselves for their families, and to provide an element of personal feeling to the song. Joel is, as
RimRod implied, very passionate about this
political concern.
It's a very
morose, mournful song, with gobs of traditional
80s pop rock melodrama. Much of the album is like this, and it's what makes it maybe his second best in my book (behind
The Stranger).