Get organic group name in a rule?
You can use the token [node:group-audience] to add the group name in your email notification. 

Here is the export of the rule I am using:

{ "rules_og_group_content_notification" : {
    "LABEL" : "OG group content notification",
    "PLUGIN" : "reaction rule",
    "OWNER" : "rules",
    "REQUIRES" : [ "og", "rules" ],
    "ON" : { "node_insert" : [] },
    "IF" : [ { "og_entity_is_group_content" : { "entity" : [ "node" ] } } ],
    "DO" : [
      { "og_get_members" : {
          "USING" : { "group_content" : [ "node" ] },
          "PROVIDE" : { "group_members" : { "group_members" : "List of group members" } }
        }
      },
      { "LOOP" : {
          "USING" : { "list" : [ "group-members" ] },
          "ITEM" : { "list_item" : "Current list item" },
          "DO" : [
            { "mail" : {
                "to" : [ "list-item:mail" ],
                "subject" : "New [node:content-type] in [node:group-audience]",
                "message" : "Hello [list-item:name],\r\n\r\nThere is a new [node:content-type] called [node:title] that belongs to [node:group-audience]: [node:url]\r\n\r\n\r\n--\r\n",
                "from" : [ "" ],
                "language" : [ "" ]
              }
            }
          ]
        }
      }
    ]
  }
}