Since a spammer decided to revive this thread...
I've been on a few different teams over the years, and each had its own method of going about it.
1293 (2004-2006): No particular pattern--it drifted around a few times.
Bob, Ockham's Raizor (and Hockham), Chomp (and Circumstance)
1618 (2007-2009): By about 2:00 PM at my first event with them, with me nursing a sore jaw from the arm whacking me and the team deciding to rename the robot on the spot, the pattern was simple: whatever the malady was, at least until their final year when we decided to get stylish.
What Robot? Uppercut, Speedy Debris, The Blackout
2815 (2009-2013): This might be the most notorious naming system in FIRST--to the point that when we gave our alliance partners shirts for picking us, they couldn't wear them to school. Y'see, 2815 was started at the University of South Carolina, home of the Gamecocks, where the fight song
goes like this. Co-founder Stephen Kowski set the precedent of honoring the mascot in the robot name, and it just stuck until the team (after my departure) moved to the high school and rebranded for 2015.
Cocked and Loaded, $@#$@#$@#$@#-A-Doodle-Doo, Cockasaurus Rex, Incocknito, Cocket Launcher
4901 (2014-2016): 4901 operated out of 2815's corner of the USC shop after they vacated. 2815 hadn't rebranded in 2014, and while both teams had the same garnet and black on that year we knew naming our robots the same way would be unabashed gimmick infringement. (And, frankly, we were having to veto more and more would-be robot names towards the end.) So we drew inspiration from
elsewhere on campus.
Sandstorm I, Sandstorm II, Sandstorm III