As for U.N.C.L.E, I guess it depends how they play it, not every organisation wants to call itself K.I.L.L, in particular one that isn't that, as far as I recall, top secret.
I've only seen the first season so far, but it's been very inconsistent about how secret (the) U.N.C.L.E. is. In the early episodes, Solo & Kuryakin are often openly telling civilians about their agency and what it does, and generally people have heard of it. There's one episode where Illya is trying to recruit Jill Ireland to help him out with a mission during a crowded party scene while there are multiple civilians (mostly members of the show's staff) well within earshot. Yet at the same time, they comport themselves like a highly secret spy agency, hiding their HQ behind the facade of a tailor shop -- yet their archenemies are perfectly well aware that that's where their HQ is located! Yet later in the season, they're playing U.N.C.L.E.'s existence much more secretly; in one episode, when they need to recruit Kathryn Hays to get close to a villain who's an old flame of hers (exactly the same reason they openly recruited Pat Crowley's character in the piot), Solo essentially kidnaps her and won't even tell her the name of the organization that's holding her captive and demanding her cooperation.
In fact if it were up to me (which it never will be) the trailer would start out a homesy tale with people in quiet rural parts talking about their problems and that maybe their uncle can help out...
Cue the music and cue the explosions
Well, there was a running gag in the show involving characters talking about getting help from a kindly uncle, or having a message for their uncle, or whatever. I suppose that was inevitable, really.