I wanted to add some information to the already-good answers, about how to properly "spell" this chord.
Because chords are made up of stacked thirds, a seventh chord built on G will have to have some form of the notes G-B?-D?-F? (I'm using '?' to represent a yet-to-be-determined accidental). In the case of a Gdim7, these would become G-B♭-D♭-F♭. But we know that in our key (C♯ minor) we call the D♭ and F♭ C♯ and E. Yes, these pitches are "enharmonically equivalent," but the Gdim7 chord has to call them D♭ and F♭, since it has to have a stack of thirds.
Fortunately, though, dim7 chords are "symmetrical" -- we can start the chord on any one of its four pitches, and it has the same shape. That means we can pick any of its notes as the root. For example, if we pick E as the root (Edim7), then the chord has to contain E-G?-B?-D?, which, in order to make a dim7 chord, works out to E-G-B♭-D♭. That's better, but we've still got that pesky D♭ in there.
You can probably see where we're going next. By starting the chord a third lower, on C♯, the notes in the chord end up being spelled as C♯-E-G?-B?. In order to make this a C♯dim7, we need to make it C♯-E-G-B♭, which is a much better fit in our key. This is why I would recommend (as did Patrx2) calling this chord a C♯dim7, or a i dim7. I haven't used hooktheory before, but perhaps a i dim7 is easier to find than a ♭IIIdim7?
A little trick to remember all of this: regardless of the accidentals and the intervals involved, almost any chord (in western, common practice music) will be built from stacked thirds. That means they have to contain adjacent notes from a sort of "circle of thirds" scheme. Triads will contain three adjacent notes, while seventh chords will contain four adjacent notes.
A? - C? - E? - G? - B? - D? - F? - A?
Note how the circle wraps around on itself (it ends where it begins). Also note how I'm careful to not specify which version of a note I'm using. That will be determined by a number of factors including the key, and the desired quality of the chord.