Originally most of the characters were named after famous celebrities. Hamish was originally called Gielgud, after John Gielgud; JP was named Bowie after 'David Bowie', and Davina was named Winslett after Kate Winslett. This is why Davina has a blue jewel-like necklace like one worn by Kate Winslett's character in Titanic (1997) and why JP has two different coloured eyes like David Bowie. Trevor is the exception here, as he was originally named "Bollocks".
The reason for all the name changes is that Channel 4 felt they weren't right for the channel's image. Davina ended up being named after Channel 4 presenter Davina McCall, who around the time of broadcast was on Channel 4 every night presenting Big Brother (2000).
JP's full name is JeanLuc Picard, named after Star Trek: The Next Generation (1987)'s captain played by Patrick Stewart. The reason for this name is because the character is JP's all-time hero and because both are completely bald.
The colour of Trevor's puppet was originally white. His colour had to be changed from white to grey because his fur flared under studio lights, and gave the lighting men headaches.
The pilot episode was recorded about 12 months before the series went into production and was never broadcast. A lot of changes were made from then. For a start, Davina doesn't appear in the original pilot episode and was added by the writers later, and the puppets for Trevor and JP look very different. The plot of the episode is that Hamish hangs himself and is later bought back to life by Trevor, who does it by electrocuting him with 50,000 volts. This plot was later used in the series two episode "Reincarnation".