But don’t all pilots have to lodge their flight plans? Surely hiding a plane in a hangar is not that easy since you would know which airport it is located in.
No, they don't. And many municipal airports aren't even manned and, outside of certain areas, aren't under direct air traffic control. I flew in a Cessna with a private pilot who landed at a municipal airport in Los Angeles Country without ever talking to anyone. He just announced his intention to land on the published radio frequency, received no objection (because no one else was around), visually confirmed the runway was clear with a flyby, then lined up on the approach path and landed. I got the sense this is the norm in civil aviation outside of major airports.
Or browse by Title 14, Chapter 1, Subchapters F & G (Aka Title 14, Parts 89 - 139)
I'm not vouching for this link in particular, but you can also search for things like Part 91 operator, Part 135 operator, etc
https://l33jets.com/resources/blog/the-difference-between-pa...