Cm. It's the 4-string version of the full barre chord generally used by acoustic players when there is a bass or electric present, or if the guitarist doesn't have strong enough or long enough fingers.
Yes it would technically be called Cm/G. Because it's a Cm with a G bass note.
Your regular major and minor chords consist of only 3 pitches, therefore you only need 3 strings to play a chord. But generally with this instrument, guitarists add more strings with the same notes to get the bigger/fuller sound.