Wikipedia article doesn't say why they used the letter Q or when they started specifically using that designation.
Interestingly, Ian Fleming, who worked in British intel, wrote many James Bond stories in the 1950s and had Q as a character. So Q designating a form of Top Secret clearance may have emerged culturally among US and UK intel personnel during the WW2.
To add to Plebbitimmigrant's reply, in past discussions elsewhere, DOE's Q clearance was brought up. Here is a useful page:
https://en.wikipedia.org/wiki/Q_clearance
Wikipedia article doesn't say why they used the letter Q or when they started specifically using that designation.
Interestingly, Ian Fleming, who worked in British intel, wrote many James Bond stories in the 1950s and had Q as a character. So Q designating a form of Top Secret clearance may have emerged culturally among US and UK intel personnel during the WW2.