The region of a glacier that is gaining mass is known as the zone of

accumulation

Explanation:

Based on the quantity of mass of the glacier, it has been partitioned into two different regions.  

At the higher end, more mass of snow gets accumulated than it loses. Which is called accumulation zone. As there is snow fall, it gets accumulated over snow of prior years. Due to this, older snow gets compressed by new layers which causes lower layered snow to convert into solid ice.

Opposite of accumulation zone is ablation zone , the zone of glacier where loss of snow is more than the accumulation. These phenomenon helps in survival of glacier by  balancing of surface mass.

Thus region of gaining mass in glacier is called zone of accumulation