If the tonal centre is G, then the key must be G something. Given just those two chords Gm and Bb - then it must be in the key of G minor.
You could only say its G Dorian if the song contains the note E but doesn't contain Eb. Is that the case?
If so then, technically, it's G Dorian - but the Dorian mode is one of the minor modes - so most people, including the sheet music publisher, will correctly say it's in the KEY of G minor and the key signature will show that it's in G minor with 2 flats (Eb and Bb). Every occurence of E natural will be shown within the music by adding the natural sign in front of every E, which is what tells us the song's mode is Dorian.
When talking about keys, major and minor are the two terms used. It's only when talking about modes that it's appropriate to call it G Dorian.
Lots of songs are modal but it doesn't affect how we call the KEY.
The Beatles' Norwegian Wood, for example is in the key of D major but its mode is actually Mixolydian (which is one of the major modes).
For most people, that's irrelevant, and rightly so.
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