diff --git a/plugins/inputs/docker/docker.go b/plugins/inputs/docker/docker.go
index c98f1f845..f5633f099 100644
--- a/plugins/inputs/docker/docker.go
+++ b/plugins/inputs/docker/docker.go
@@ -416,7 +416,9 @@ func (d *Docker) gatherContainer(
 	daemonOSType := r.OSType
 
 	// use common (printed at `docker ps`) name for container
-	tags["container_name"] = strings.TrimPrefix(v.Name, "/")
+	if v.Name != "" {
+		tags["container_name"] = strings.TrimPrefix(v.Name, "/")
+	}
 
 	// Add labels to tags
 	for k, label := range container.Labels {
@@ -442,6 +444,7 @@ func (d *Docker) gatherContainer(
 			}
 		}
 	}
+
 	if info.State != nil {
 		tags["container_status"] = info.State.Status
 		statefields := map[string]interface{}{
@@ -458,14 +461,14 @@ func (d *Docker) gatherContainer(
 			statefields["finished_at"] = container_time.UnixNano()
 		}
 		acc.AddFields("docker_container_status", statefields, tags, time.Now())
-	}
 
-	if info.State.Health != nil {
-		healthfields := map[string]interface{}{
-			"health_status":  info.State.Health.Status,
-			"failing_streak": info.ContainerJSONBase.State.Health.FailingStreak,
+		if info.State.Health != nil {
+			healthfields := map[string]interface{}{
+				"health_status":  info.State.Health.Status,
+				"failing_streak": info.ContainerJSONBase.State.Health.FailingStreak,
+			}
+			acc.AddFields("docker_container_health", healthfields, tags, time.Now())
 		}
-		acc.AddFields("docker_container_health", healthfields, tags, time.Now())
 	}
 
 	parseContainerStats(v, acc, tags, container.ID, d.PerDevice, d.Total, daemonOSType)
diff --git a/plugins/inputs/docker/docker_test.go b/plugins/inputs/docker/docker_test.go
index b97c34b6b..968dbf725 100644
--- a/plugins/inputs/docker/docker_test.go
+++ b/plugins/inputs/docker/docker_test.go
@@ -3,7 +3,9 @@ package docker
 import (
 	"context"
 	"crypto/tls"
+	"io/ioutil"
 	"sort"
+	"strings"
 	"testing"
 
 	"github.com/influxdata/telegraf/testutil"
@@ -747,3 +749,69 @@ func TestContainerStateFilter(t *testing.T) {
 		})
 	}
 }
+
+func TestContainerName(t *testing.T) {
+	tests := []struct {
+		name       string
+		clientFunc func(host string, tlsConfig *tls.Config) (Client, error)
+		expected   string
+	}{
+		{
+			name: "container stats name is preferred",
+			clientFunc: func(host string, tlsConfig *tls.Config) (Client, error) {
+				client := baseClient
+				client.ContainerListF = func(context.Context, types.ContainerListOptions) ([]types.Container, error) {
+					var containers []types.Container
+					containers = append(containers, types.Container{
+						Names: []string{"/logspout/foo"},
+					})
+					return containers, nil
+				}
+				client.ContainerStatsF = func(ctx context.Context, containerID string, stream bool) (types.ContainerStats, error) {
+					return types.ContainerStats{
+						Body: ioutil.NopCloser(strings.NewReader(`{"name": "logspout"}`)),
+					}, nil
+				}
+				return &client, nil
+			},
+			expected: "logspout",
+		},
+		{
+			name: "container stats without name uses container list name",
+			clientFunc: func(host string, tlsConfig *tls.Config) (Client, error) {
+				client := baseClient
+				client.ContainerListF = func(context.Context, types.ContainerListOptions) ([]types.Container, error) {
+					var containers []types.Container
+					containers = append(containers, types.Container{
+						Names: []string{"/logspout"},
+					})
+					return containers, nil
+				}
+				client.ContainerStatsF = func(ctx context.Context, containerID string, stream bool) (types.ContainerStats, error) {
+					return types.ContainerStats{
+						Body: ioutil.NopCloser(strings.NewReader(`{}`)),
+					}, nil
+				}
+				return &client, nil
+			},
+			expected: "logspout",
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			d := Docker{
+				newClient: tt.clientFunc,
+			}
+			var acc testutil.Accumulator
+			err := d.Gather(&acc)
+			require.NoError(t, err)
+
+			for _, metric := range acc.Metrics {
+				// This tag is set on all container measurements
+				if metric.Measurement == "docker_container_mem" {
+					require.Equal(t, tt.expected, metric.Tags["container_name"])
+				}
+			}
+		})
+	}
+}