This can be called an F Diminished scale. In classical music theory it would usually be called an Octatonic Scale. It is a mode of limited transposition (it has a constantly repeating tone-semitone interval pattern). It has a number of interesting properties, for instance, the scale contains a pair of diminished 7th arpeggios, a semitone apart.
For any particular starting pitch, there are two possible Octatonic scales: one starting with a tone; one starting with a semitone. Interestingly, there are only three possible Octatonic scales (if you consider them by pitch set, and ignore the starting note). For instance, the scales starting: E-F; F-Gb; F#-G. All other Octatonic scales will contain EXACTLY the same notes as one of these scales (hence "limited transposition").
As this scale has 8 notes, two of the pitch names always have to have the same letter (Ab and A in your example). This is also sometimes reflected in chord types associated with this scale; for instance the Gb, Ab and A in this chord would make it a b9/#9 chord, even though, in theory, it has two thirds.