I've always thought that they named themselves after this char.

https://en.wikipedia.org/wiki/Q_(James_Bond)

Q (James Bond)

Q is a fictional character in the James Bond films and film novelisations. Q (standing for Quartermaster), like M, is a job title rather than a name. He is the head of Q Branch (or later Q Division), the fictional research and development division of the British Secret Service. The use of letters as pseudonyms for senior officers in the British Secret Intelligence Service was started by its first director Captain Sir Mansfield George Smith-Cumming (1859–1923) who signed himself with a C written in green ink.[1]

Q has appeared in 21 of the 24 Eon Productions's James Bond films, the exceptions being Live and Let Die, Casino Royale and Quantum of Solace. The character was also featured in both non-Eon Bond films, Casino Royale (1967) and Never Say Never Again (1983).