Game maps should give you somewhere to record your own discoveries, including the ones you haven't understood yet. A personal marker with a few words could preserve the reason a place interested you without turning that place into an objective the game has assigned.
Imagine exploring a valley and spotting a narrow tunnel above the river. You cannot reach its entrance from where you're standing, but you want to investigate another approach. A note reading “Tunnel above river; try the northern slope” would preserve that idea. It wouldn't tell you whether the tunnel contains treasure, leads anywhere useful or can even be entered.
That uncertainty is worth keeping. The map I'd want would help me remember my own investigation while leaving its outcome open. It would let me distinguish something I saw from something I suspect, and change my mind without treating the abandoned theory as unfinished work.
Let a note remain a theory
In that imaginary valley, an automatic marker saying “Hidden passage” would already reveal more than the player has established. A personal note saying “Possible entrance?” would make a different promise: this is somewhere you chose to examine, not a destination whose importance has been confirmed.
The distinction should survive the way the marker looks. Player notes ought to be recognizable as player notes, rather than borrowing the appearance of verified quest objectives. Otherwise, your guess could acquire an authority it hasn't earned simply because the interface presents it confidently.
A useful annotation would also preserve the observation behind a theory. “Gate has a circular socket” is more informative than “come back later.” If you subsequently find a round object, you can decide whether the connection is worth testing. The note doesn't need to identify the correct object or tell you that the gate is a puzzle at all.
Sometimes the investigation should end with nothing. You reach the tunnel and discover an ordinary dead end. Let that be a satisfactory answer. You could remove the marker or change it to “checked,” without a completion meter suggesting there must be another reward to collect. Recording your curiosity shouldn't create a contract to make every detour worthwhile.
Make a short note easy to place
I wouldn't want writing a paragraph to become the price of marking a map. Start with a few recognizable symbols that the player can give consistent meanings: a question mark for something unexplored, a barrier for an obstruction, perhaps a flag for a preferred route. A short annotation should be available when the symbol alone would leave too much to reconstruct.
The important words are the ones that explain the next decision. “Entrance above this point” could prevent a two-dimensional pin from sending you back to the wrong level. “Return from the river” records a route you intend to test. Neither requires a diary entry or a catalogue of everything visible on screen.
For a controller interface, I'd prioritize placing the marker accurately, choosing its symbol and getting straight back to the game. Text can be an extra step. Players should be able to move or revise a note when their understanding changes, without deleting it and rebuilding it from scratch.
There is a tradeoff: personal marks can obscure the map they are meant to explain. I'd keep the symbols visible but show the longer annotation only when selected. A separate control to hide personal notes would let you inspect the underlying geography without discarding your work. The design should remain useful with three notes, rather than encouraging you to tag every corner.
Leave room for unfinished exploration
This proposal wouldn't suit every adventure equally. If remembering a route unaided is a deliberate part of the challenge, adding a detailed annotation system would change that demand. A small, linear game might have little reason to support one. The case is strongest where you want to choose your own detours and keep several possible routes in mind.
Shared maps would need another distinction. Your note about a suspicious wall could spoil a discovery for a friend who hasn't reached it. Personal observations should stay private unless you choose to share them. Even then, a teammate's theory should remain attributable to that teammate, not silently become a fact everyone is expected to act on.
You can use the same approach wherever a game already supports custom markers, or in a separate notebook. Record what caught your attention and the approach you want to try. Add a question mark when you're guessing. Avoid copying a guide's answer into the note if investigating for yourself is the part you want to preserve.
When you return to a marked place, allow yourself to revise or discard the idea. The useful result might be finding another route, ruling one out or deciding you'd rather explore somewhere else. A personal map should preserve your reasons for looking, while leaving you free to decide what deserves another look.