but I don't know whether it would be safer to make, say, a police officer aware that you're just 'Q' (and thus reveal a confidential identity) or give your real name and potentially put yourself or family in danger. I suppose a false name would come in handy there.

I'd guess that the current version of Q has a false name for everyday purposes. Although my guess is that the past versions of Q probably used their real names.

I feel like Skyfall updated Q to fit the changing world where information is available via a keystroke and accessible cameras are everywhere.

With surveillance being that ubiquitous, having a fake name probably helps. Especially since Q could help an enemy hack into the British government and thus runs the risk of having more eyes looking for him. Back when Q was more a gadget master, I don't know how many baddies would be out to actually compromise him.