The name is the primary ´title´ of the photo gallery group (groups contain categories that in turn contain albums). It will be displayed to all uses as the identifier of the specific group.

Choose a self-evident name/title for the group that makes a general distinction between the other groups. In many simple implementations there may only be one group. In more complex cases where there will be many photos there might be several - it would be rare to ever have more then a few groups though.