diff --git a/docker/bash.sh b/docker/bash.sh
index 372cfded8f89..cbd71870747c 100755
--- a/docker/bash.sh
+++ b/docker/bash.sh
@@ -22,7 +22,7 @@
 #
 # Usage: docker/bash.sh [-i|--interactive] [--net=host] [-t|--tty]
 #          [--mount MOUNT_DIR] [--repo-mount-point REPO_MOUNT_POINT]
-#          [--dry-run]
+#          [--dry-run] [--name NAME]
 #          <DOCKER_IMAGE_NAME> [--] [COMMAND]
 #
 # Usage: docker/bash.sh <CONTAINER_NAME>
@@ -40,7 +40,7 @@ function show_usage() {
     cat <<EOF
 Usage: docker/bash.sh [-i|--interactive] [--net=host] [-t|--tty]
          [--mount MOUNT_DIR] [--repo-mount-point REPO_MOUNT_POINT]
-         [--dry-run]
+         [--dry-run] [--name NAME]
          <DOCKER_IMAGE_NAME> [--] [COMMAND]
 
 -h, --help
@@ -85,6 +85,11 @@ Usage: docker/bash.sh [-i|--interactive] [--net=host] [-t|--tty]
 
     Print the docker command to be run, but do not execute it.
 
+--name
+
+    Set the name of the docker container, and the hostname that will
+    appear inside the container.
+
 DOCKER_IMAGE_NAME
 
     The name of the docker container to be run.  This can be an
@@ -118,6 +123,7 @@ USE_NET_HOST=false
 DOCKER_IMAGE_NAME=
 COMMAND=bash
 MOUNT_DIRS=( )
+CONTAINER_NAME=
 
 # TODO(Lunderberg): Remove this if statement and always set to
 # "${REPO_DIR}".  The consistent directory for Jenkins is currently
@@ -180,6 +186,15 @@ while (( $# )); do
             shift
             ;;
 
+        --name)
+            if [[ -n "$2" ]]; then
+                CONTAINER_NAME="$2"
+                shift 2
+            else
+                parse_error 'ERROR: --name requires a non empty argument'
+            fi
+            ;;
+
         --dry-run)
             DRY_RUN=true
             shift
@@ -312,6 +327,11 @@ if ${TTY}; then
     DOCKER_FLAGS+=( --tty )
 fi
 
+# Setup the docker name and the hostname inside the container
+if [[ ! -z "${CONTAINER_NAME}" ]]; then
+    DOCKER_FLAGS+=( --name ${CONTAINER_NAME} --hostname ${CONTAINER_NAME})
+fi
+
 # Expose external directories to the docker container
 for MOUNT_DIR in ${MOUNT_DIRS[@]+"${MOUNT_DIRS[@]}"}; do
     DOCKER_MOUNT+=( --volume "${MOUNT_DIR}:${MOUNT_DIR}" )
diff --git a/docker/build.sh b/docker/build.sh
index 3b58bcc52a75..4e1a9b346895 100755
--- a/docker/build.sh
+++ b/docker/build.sh
@@ -23,7 +23,8 @@
 # Usage: build.sh <CONTAINER_TYPE> [--tag <DOCKER_IMAGE_TAG>]
 #                [--dockerfile <DOCKERFILE_PATH>] [-it]
 #                [--net=host] [--cache-from <IMAGE_NAME>]
-#                [--context-path <CONTEXT_PATH>] [<COMMAND>]
+#                [--name CONTAINER_NAME] [--context-path <CONTEXT_PATH>]
+#                [<COMMAND>]
 #
 # CONTAINER_TYPE: Type of the docker container used the run the build,
 #                 e.g. "ci_cpu", "ci_gpu"
@@ -38,6 +39,9 @@
 # IMAGE_NAME: An image to be as a source for cached layers when building the
 #             Docker image requested.
 #
+# CONTAINER_NAME: The name of the docker container, and the hostname that will
+#                 appear inside the container.
+#
 # CONTEXT_PATH: Path to be used for relative path resolution when building
 #               the Docker images.
 #
@@ -95,6 +99,12 @@ else
     echo "Using default context path: ${DOCKER_CONTEXT_PATH}"
 fi
 
+if [[ "$1" == "--name" ]]; then
+    CI_DOCKER_EXTRA_PARAMS+=("--name ${2} --hostname ${2}")
+    echo "Using container name ${2}"
+    shift 2
+fi
+
 if [[ ! -f "${DOCKERFILE_PATH}" ]]; then
     echo "Invalid Dockerfile path: \"${DOCKERFILE_PATH}\""
     exit 1