If we need to analyse a work written strictly in Am , I think VI and VII are clear enough.
If there is a modulation between Am and A , and we want to keep A as root, I would use ♭VI for F and VI for F# .
Same if any modal interchange occurs, e.g.: A F#m F GI vi ♭VI ♭VII
Regarding the occurrences of
F# and G# as chord roots, it really depends on the context - usually F# would appear in D first inversion (so IV/6 ) or as V/V/V , while G# would be in V/6 or in viio .
If both G AND G#dim join the game, I would use VII and #viio respectively.
music.stackexchange.com/users/35439/moonwave99
Usage varies.
But I'd suggest that the only unambiguous method is to name chords, whether as chord symbols or Roman numerals in relation to the major key.
Whether the key is C major or C minor, C,E,G is 'C', C, E♭,G is 'Cm'.
Similarly, C,E,G is 'I', C,
E♭,G is 'i'.
B♭, D, F is '♭VII', B♭, D♭,
F is '♭vii'.
There will be disagreement about this!
music.stackexchange.com/users/17003/Laurence Payne
I think it's important to remember a vital distinction here: an accidental before the Roman numeral applies to the root of the chord.
An accidental after the Roman numeral is figured bass.
So in A minor, F major is VI, because F is scale-degree 6 in A minor.
Only in A major would we need to clarify this F-major chord as ♭VI (or ♮VI if we want to be really fussy).
♭VI in A minor would actually be F♭ (=
E!)
major.
But neither one of these is to be confused with VI ♯ in A major, which would be an F♯-major chord.
Here the accidental applies to the third above the bass, thereby making this a collection of {F♯, A♯, C♯}.
music.stackexchange.com/users/21766/Richard
It really depends on the convention one adopts.
Some music theory symbols are pretty standard, but one sees variances among textbooks, theorists, and the style they are analyzing.
I'd say the most standard pattern in American "classical theory" textbooks of the past 40-50 years is to assume in A minor that VI means F major, VII means G major, and vii o means G♯dim.
I've seen some textbooks that tack on a flat or natural to VII (i.e., ♭VII or even ♮VII to accord with the key signature) to refer to G major, but most books probably omit it.
In classical theory, a chord on the seventh scale degree is just assumed by default to be built on the subtonic if major and on the leading tone if diminished.
However, that assumption may not be true of pop/jazz theory books, where Roman numerals with accidentals are more commonly employed and there are fewer assumptions about the implications and function of Roman numerals.
For the sixth degree, VI in minor is just assumed in classical theory to be built on the minor sixth scale degree, so no accidental is necessary.
In fact, as Richard points out, putting a flat on it could confuse some people -- though again, I think that's dependent on convention.
I'm pretty sure I've seen at last one book (I think in pop or jazz theory)
that assumed the major scale was the scale, so any deviation from it was notated with an accidental.
Thus ♭VI would be necessary to designate F major in that system for any key or mode based on A.
(I'd personally avoid using a symbol like ♭VI in a minor key, to avoid confusion, but again it depends on the convention you're working with.)
In the end, I agree with Laurence Payne: if you want to be absolutely clear what chord you're referencing and the specific notes, use a chord symbol (like Fmajor) rather than a Roman numeral.
Roman numerals are a shortcut to designate function ( not just label chords, though many people confuse this), and the function of a VI or VII or whatever should be pretty clear from context.
music.stackexchange.com/users/63809/Athanasius
I learned the classical way of naming chords and also a more modern way which I prefer where everything is literally spelled out in relation to the root note of the keys regardless of whether it’s major or minor.
There are no small letters and all relationships are spelled out like the way intervals are named.
Examples:
Diatonic major chords: I IIm IIIm IV V VIm VIIo Eb in the key of either C or Cm:
bIII Amaj7 in the key of G or Gm: IImaj7 Em7b5 in the key of D or Dm: IIm7b5 Fmaj7 in the key of E or Em:
bIImaj7
I prefer this method because there is no doubt as to what the interval from the home key or what the quality of the chord is.
music.stackexchange.com/users/67196/John Belzaguy
We know that in minor  keys  the 6th and 7th notes can be 'basic' or a semitone higher.  By 'basic', I mean they obey the key signature. So, in key Am, would chords F and G be better portrayed as VI and VII, or as ♭VI and ♭VII respectively?  Or is there a more accurate, less ambiguous way?
Specific Roman Numeral naming for chords F and G in key Am
music.stackexchange.com
<chords><chord-theory>
music.stackexchange.com/questions/104397
music.stackexchange.com/users/2808/Tim
 I'd say the most standard pattern in American "classical theory" textbooks of the past 40-50 years is to assume in A minor that VI means F major, VII means G major, and vii o  means G♯dim. While, For the sixth degree, VI in minor is just assumed in classical theory to be built on the minor sixth scale degree, so no accidental is necessary.   A minor VI means F major, VII means G major, and vii o  means G♯dim.  
The most standard pattern in American "classical theory" textbooks of the past 40-50 years is to assume in A minor that VI means F major, VII means G major, and vii o  means G♯dim.  