Why Jessica?
One of Jessica's parents must have been a big Shakespeare buff. That's the only reason I can think of that a girl being born in the 1920s or 30s would have been given that name. (I actually looked this up. Only once during those 20 years did the name ever break the top 1000 in popularity here in the US.)
Either that, or the writers just chose one of the more popular names of the 1980s at random. But I like the Shakespeare idea.