Expose ContainerName in Docker provider

docs/content/providers/docker.md

@@ -440,10 +440,11 @@ _Optional, Default=```Host(`{{ normalize .Name }}`)```_
 
 The `defaultRule` option defines what routing rule to apply to a container if no rule is defined by a label.
 
-It must be a valid [Go template](https://pkg.go.dev/text/template/), and can use
-[sprig template functions](https://masterminds.github.io/sprig/).
-The container service name can be accessed with the `Name` identifier,
-and the template has access to all the labels defined on this container.
+It must be a valid [Go template](https://pkg.go.dev/text/template/),
+and can use [sprig template functions](https://masterminds.github.io/sprig/).
+The container name can be accessed with the `ContainerName` identifier.
+The service name can be accessed with the `Name` identifier.
+The template has access to all the labels defined on this container with the `Labels` identifier.
 
 ```yaml tab="File (YAML)"
 providers:

pkg/provider/docker/config.go

@@ -75,9 +75,11 @@ func (p *Provider) buildConfiguration(ctx context.Context, containersInspected [
 
 		model := struct {
 			Name          string
+			ContainerName string
 			Labels        map[string]string
 		}{
 			Name:          serviceName,
+			ContainerName: strings.TrimPrefix(container.Name, "/"),
 			Labels:        container.Labels,
 		}