For one thing, Dorian is a mode, not a key .

@Tim -- I subscribe to the paradigm that a downvote indicates that the question is unlikely to be of interest or value to the general readership. I'm not using it as an ad-hominem attack.

@Tim, fair enough.. I'll remove

@CarlWitthoft - Takes a special sort of person! Thank you.

It's six in the morning, and my day has already been made. Thanks guys! @CarlWitthoft and Tim

I think you want to use a wording that tells the number of accidentals "...key signature of one sharp" and use "major" or "minor." So... G major has a key signature of one sharp. If you say "key signature of G" we are left wondering: major or minor? Also, if you say something like E minor has a key signature of G major, we still don't know how many accidentals.

@MichaelCurtis - I keep saying this. There has to be a better term than 'accidental'. An accidental is something put in to change a stated note in the key sig. It really shouldn't be the name for # or b at the beginning! But what?

@Tim, I know what you mean. I'm not accidentally changing F to F# to make G major!

@MichaelCurtis - not a criticism of your answer! But the # and b in a key sig. are there on purpose, not accidentally!

@Tim, right! My comment was a joke :-)

@MichaelCurtis - I know. It didn't fall b 'cos I'm quite #. But the question still remains...

Isn't it normal and clear to say "D major has the key signature of two sharps, G Dorian has the key signature of one flat", and so forth? That's what I do.

@ScottWallace - so calling it 'key sig.' rather than 'accidentals at the start'? Seems good. Question - is, say, D Dorian a 'key'? I'm really not sure if that's the correct term.

Had to smile when you said 'above the key sig. of C'. Nice one!

Good point about me calling D Dorian a key, Tim. I’m being provocative again. If we call A minor a key, why not the others?

Only just got the double meaning of “putting D dorian above the key signature of C” :-) Yes, I mean both.

I was alluding to 'how do we know there's a key sig. actually there?' as C has an invisible one...

@Tim - at least the way I'm used to using the terms, "accidental" means "a tone within a piece that's been altered away from the key (or mode) of the piece, by means of a sharp (or flat, etc) sign". I wouldn't call the F# and C# signs in a key (or mode) signature "accidentals". And while I find the distinction between "keys" and "modes" to be an historical artificiality, I usually go along with convention and say "the key of C major" and "the mode of D dorian". I don't know what's considered "correct", but as far as I know, there's no "correct" usage that doesn't fall apart somewhere.