This term originated when the fashion of blog aggregators hit the hacker community, hence the “hacker” part.
Jakub Steiner, a GNOME artist, had created several whole body cutouts that originally appeared on the Art.GNOME.org website. A couple of years later, Jeff Waugh launched Planet GNOME, a blog aggregator of GNOME programmmers and contributors. Luke Stroven suggested that Jeff use the images created by Steiner with posts by those writers. Stroven then created a bunch of images that depicted the heads of people on Planet GNOME. Waugh coined the term hackergotchi after seeing the collection of heads Stroven created.
The “-gotchi” part seems to be a reference to the term Tamagotchi.