diff --git a/enos/modules/docker_openssh_server/main.tf b/enos/modules/docker_openssh_server/main.tf
index 833e030f85..ae144b44a4 100644
--- a/enos/modules/docker_openssh_server/main.tf
+++ b/enos/modules/docker_openssh_server/main.tf
@@ -99,6 +99,10 @@ output "address" {
   value = docker_container.openssh_server.network_data[0].ip_address
 }
 
+output "container_name" {
+  value = var.container_name
+}
+
 output "port" {
   value = "2222"
 }
diff --git a/enos/modules/docker_openssh_server_ca_key/main.tf b/enos/modules/docker_openssh_server_ca_key/main.tf
index 7a63e0cd54..6ea8e8a31b 100644
--- a/enos/modules/docker_openssh_server_ca_key/main.tf
+++ b/enos/modules/docker_openssh_server_ca_key/main.tf
@@ -123,6 +123,10 @@ output "address" {
   value = docker_container.openssh_server.network_data[0].ip_address
 }
 
+output "container_name" {
+  value = var.container_name
+}
+
 output "port" {
   value = "2222"
 }
diff --git a/enos/modules/test_e2e_docker/main.tf b/enos/modules/test_e2e_docker/main.tf
index 772f225214..6bfb5dc338 100644
--- a/enos/modules/test_e2e_docker/main.tf
+++ b/enos/modules/test_e2e_docker/main.tf
@@ -84,6 +84,11 @@ variable "target_address" {
   type        = string
   default     = ""
 }
+variable "target_container_name" {
+  description = "Container Name of target"
+  type        = string
+  default     = ""
+}
 variable "target_port" {
   description = "Port of target"
   type        = string
@@ -310,6 +315,7 @@ resource "enos_local_exec" "run_e2e_test" {
     E2E_PASSWORD_AUTH_METHOD_ID   = var.auth_method_id
     E2E_PASSWORD_ADMIN_LOGIN_NAME = var.auth_login_name
     E2E_PASSWORD_ADMIN_PASSWORD   = var.auth_password
+    E2E_TARGET_CONTAINER_NAME     = var.target_container_name
     E2E_TARGET_ADDRESS            = var.target_address
     E2E_TARGET_PORT               = var.target_port
     E2E_SSH_USER                  = var.target_user
diff --git a/enos/modules/test_e2e_docker/test_runner.sh b/enos/modules/test_e2e_docker/test_runner.sh
index 9e8c330f55..1e77279176 100644
--- a/enos/modules/test_e2e_docker/test_runner.sh
+++ b/enos/modules/test_e2e_docker/test_runner.sh
@@ -17,6 +17,7 @@ docker run \
     -e "E2E_PASSWORD_AUTH_METHOD_ID=$E2E_PASSWORD_AUTH_METHOD_ID" \
     -e "E2E_PASSWORD_ADMIN_LOGIN_NAME=$E2E_PASSWORD_ADMIN_LOGIN_NAME" \
     -e "E2E_PASSWORD_ADMIN_PASSWORD=$E2E_PASSWORD_ADMIN_PASSWORD" \
+    -e "E2E_TARGET_CONTAINER_NAME=$E2E_TARGET_CONTAINER_NAME" \
     -e "E2E_TARGET_ADDRESS=$E2E_TARGET_ADDRESS" \
     -e "E2E_TARGET_PORT=$E2E_TARGET_PORT" \
     -e "E2E_SSH_USER=$E2E_SSH_USER" \