Peake, who is set to become the first Briton to visit the ISS, took time out from his training to talk to school groups and hear some of their suggestions for the mission's name.
Minister for Universities and Science David Willetts said: "The naming competition is just one of many opportunities for young people to get involved in a mission that will shape the future of Britain’s space programme and inspire generations.”
Peake said: “The ISS is a cutting edge research laboratory that is pushing the boundaries of what is scientifically, technically and humanly possibly. My 6 month stay onboard mankind's outpost in space is going to be both challenging and incredibly exciting."
The winning entrant will see their suggested name become the mission's official title and they will receive a signed mission logo.
The UK's first official astronaut Major Tim Peake told ITV News he wanted to continue Commander Chris Hadfield's "great work" of tweeting pictures from space but would not "inflict" his singing voice on the world.
Cdr Hadfield, from Canada, performed a cover of David Bowie's song Space Oddity while he was onboard the International Space Station.
Maj Peake said he was "delighted" with his mission to space and added that his family were "thrilled" for him.