diff --git a/.gitignore b/.gitignore
index 08e4c0323bf91..dd898d0a51aa3 100644
--- a/.gitignore
+++ b/.gitignore
@@ -12,7 +12,7 @@ jetpack_vendor/
 .DS_Store
 *.code-workspace
 *.swp
-# Custom environment for docker-compose (used by docker-compose.yml)
+# Custom environment for Docker compose (used by docker-compose.yml)
 /.env
 /tools/docker/compose-extras.yml
 /tools/docker/compose-volumes.yml
@@ -34,7 +34,7 @@ npm-debug.log
 phpcs.xml
 .phpunit.result.cache
 
-## Things for docker-composer
+## Things for Docker compose
 /tools/docker/data/*
 !/tools/docker/data/.gitkeep
 !/tools/docker/data/ssh.keys/
diff --git a/tools/check-development-environment.sh b/tools/check-development-environment.sh
index 45f4e16adb5e0..188c4323b66a6 100755
--- a/tools/check-development-environment.sh
+++ b/tools/check-development-environment.sh
@@ -358,19 +358,23 @@ if [[ -z "$BIN" ]]; then
 else
 	success "yes"
 
-	checking '[optional] Docker-compose is available'
-	BIN="$(command -v docker-compose)"
-	if [[ -z "$BIN" ]]; then
+	checking '[optional] Docker compose is available'
+	AS=
+	if docker compose version &>/dev/null; then
+		VER="$(docker compose version 2>/dev/null | sed -n -E 's/^(docker-compose|Docker Compose) version v?([0-9]+\.[0-9]+\.[0-9a-zA-Z.-]+)(, .*|\+.*)?$/\2/p')"
+		AS='docker compose'
+	elif BIN="$(command -v docker-compose)"; then
+		VER="$(docker-compose --version 2>/dev/null | sed -n -E 's/^(docker-compose|Docker Compose) version v?([0-9]+\.[0-9]+\.[0-9a-zA-Z.-]+)(, .*|\+.*)?$/\2/p')"
+		AS='docker-compose'
+	fi
+	if [[ -z "$AS" ]]; then
 		warning "no" 'docker-supported-recommended'
+	elif [[ -z "$VER" ]]; then
+		warning "yes (as '$AS', version unknown)"
+	elif version_compare "$VER" "1.28"; then
+		success "yes (as '$AS', version $VER)"
 	else
-		VER="$(docker-compose --version 2>/dev/null | sed -n -E 's/^(docker-compose|Docker Compose) version v?([0-9]+\.[0-9]+\.[0-9a-zA-Z.-]+)(, .*)?$/\2/p')"
-		if [[ -z "$VER" ]]; then
-			warning "yes (version unknown)"
-		elif version_compare "$VER" "1.28"; then
-			success "yes (version $VER)"
-		else
-			warning "yes (version $VER)" '' "Docker-compose at $BIN is version $VER. Version 1.28 or later is recommended."
-		fi
+		warning "yes (as '$AS', version $VER)" '' "Docker compose at $BIN is version $VER. Version 1.28 or later is recommended."
 	fi
 
 	checking '[optional] Docker is running'
diff --git a/tools/cli/commands/docker.js b/tools/cli/commands/docker.js
index 78fcdac8daf9d..b3257b4123766 100644
--- a/tools/cli/commands/docker.js
+++ b/tools/cli/commands/docker.js
@@ -4,6 +4,11 @@ import chalk from 'chalk';
 import * as envfile from 'envfile';
 import { dockerFolder, setConfig } from '../helpers/docker-config.js';
 
+/**
+ * How to run Docker compose.
+ */
+let dockerComposeCmd = null;
+
 /**
  * Sets default options that are common for most of the commands
  *
@@ -154,16 +159,28 @@ const checkProcessResult = res => {
 };
 
 /**
- * Executor for `docker-compose` commands
+ * Executor for `docker compose` commands
  *
  * @param {object} argv - Yargs
  * @param {Array} opts - Array of arguments
  * @param {object} envOpts - key-value pairs of the ENV variables to set
  */
 const composeExecutor = ( argv, opts, envOpts ) => {
-	const res = executor( argv, () =>
-		shellExecutor( argv, 'docker-compose', opts, { env: envOpts } )
-	);
+	if ( dockerComposeCmd === null ) {
+		if ( argv.v ) {
+			console.log( chalk.green( 'Checking how to run Docker compose' ) );
+		}
+		if ( spawnSync( 'docker', [ 'compose', 'version' ], { stdio: 'ignore' } ).status === 0 ) {
+			dockerComposeCmd = [ 'docker', 'compose' ];
+		} else if ( spawnSync( 'docker-compose', [ '--version' ], { stdio: 'ignore' } ).status === 0 ) {
+			dockerComposeCmd = [ 'docker-compose' ];
+		} else {
+			console.error( chalk.red( `Neither 'docker compose' nor 'docker-compose' is available.` ) );
+			process.exit( 1 );
+		}
+	}
+	const [ cmd, ...args ] = dockerComposeCmd.concat( opts );
+	const res = executor( argv, () => shellExecutor( argv, cmd, args, { env: envOpts } ) );
 	checkProcessResult( res );
 };
 
@@ -501,7 +518,7 @@ const execJtCmdHandler = argv => {
 		const dockerPs = spawnSync(
 			'docker',
 			[
-				"ps --filter 'name=jetpack_dev_wordpress' --filter 'status=running' --format='{{.ID}} {{.Names}}'",
+				"ps --filter 'name=jetpack_dev[_-]wordpress' --filter 'status=running' --format='{{.ID}} {{.Names}}'",
 			],
 			{
 				encoding: 'utf8',
diff --git a/tools/docker/README.md b/tools/docker/README.md
index 0d53ad61a1825..ff3ed2d622385 100644
--- a/tools/docker/README.md
+++ b/tools/docker/README.md
@@ -29,7 +29,7 @@ cp tools/docker/default.env tools/docker/.env
 
 Anything you put in `.env` overrides values in `default.env`. You should modify all the password fields for security, for example.
 
-**Note**: in older versions of docker-compose (earlier than 1.28), you'll need to place that file at the root of the monorepo.
+**Note**: in older versions of Docker compose (earlier than 1.28), you'll need to place that file at the root of the monorepo.
 
 ## Quick start
 
@@ -59,7 +59,7 @@ WordPress’ `WP_SITEURL` and `WP_HOME` constants are configured to be dynamic i
 ## Custom mounts, environment Variables, `.env` Files, and Ports
 
 You can control some of the behavior of Jetpack's Docker configuration with environment variables. Note, though, that there are two types of environments:
-1. The host environment in which the `jetpack docker *` (`docker-compose`) commands run when creating/managing the containers.
+1. The host environment in which the `jetpack docker *` (Docker compose) commands run when creating/managing the containers.
 2. The containers' environments.
 
 ### Host Environment
@@ -90,7 +90,7 @@ Users can extended these configurations further via override config file `tools/
 The default config file `tools/docker/jetpack-docker-config-default.yml` includes inline comments explaining the structure of config, but here's quick overview. The configuration is grouped per environment type: `default`, `dev`, `e2e`. Each type may define `volumeMappings` and `extras`:
 
 * `volumeMappings` - list of key value pairs which defines local directory mappings with following structure: local_path: wordpress_container_path
-* `extras` - basically any other configuration that is supported by `docker-compose`
+* `extras` - basically any other configuration that is supported by Docker compose.
 
 ## Working with containers
 
@@ -144,7 +144,7 @@ Stops all containers.
 jetpack docker down
 ```
 
-Will stop all of the containers created by this docker-compose configuration and remove them, too. It won’t remove the images. Just the containers that have just been stopped.
+Will stop all of the containers created by this Docker compose configuration and remove them, too. It won’t remove the images. Just the containers that have just been stopped.
 
 ### Running unit tests
 
diff --git a/tools/docker/compose-volumes.yml.sample b/tools/docker/compose-volumes.yml.sample
index 0bcc04316784f..89cd00b49d858 100644
--- a/tools/docker/compose-volumes.yml.sample
+++ b/tools/docker/compose-volumes.yml.sample
@@ -5,7 +5,7 @@
 ########
 
 ## List volumes for plugins, themes, and so on here. Format is a sequence as appropriate for
-## docker-compose's service.volumes. In brief,
+## Docker compose's service.volumes. In brief,
 ##  - Begin each line with a "-" followed by a space.
 ##  - Line consists of two fields, local path and docker path, separated by a colon.
 ##  - Local path may be absolute, or relative to this file by beginning with "./" or "../".
diff --git a/tools/docker/docker-compose.yml b/tools/docker/docker-compose.yml
index dc8782599b379..9a1910556a680 100644
--- a/tools/docker/docker-compose.yml
+++ b/tools/docker/docker-compose.yml
@@ -23,7 +23,7 @@ services:
 
   ## - The container wordpress is a very basic but custom container with WordPress and all of the tools we need
   ##   for development.
-  ## - The container will be named jetpack_wordpress for easy reference when running docker/docker-compose commands
+  ## - The container will be named jetpack_dev_wordpress_1 or jetpack_dev-wordpress-1 (depending on your Docker compose version) for easy reference when running Docker commands
   ##
   ## Here we map the following:
   ##  - The docker/wordpress-develop directory where we'll get WordPress source code with unit tests
diff --git a/tools/docker/jetpack-docker-config-default.yml b/tools/docker/jetpack-docker-config-default.yml
index b8592a6b13b72..8498d44384cbd 100644
--- a/tools/docker/jetpack-docker-config-default.yml
+++ b/tools/docker/jetpack-docker-config-default.yml
@@ -9,7 +9,7 @@ default:
     tools/docker/mu-plugins: /var/www/html/wp-content/mu-plugins
 
   # Extra configuration (none by default). Anything set under this key will be written out as
-  # an extra docker-compose configuration file.
+  # an extra Docker compose configuration file.
   extras:
 
 # Dev environment overrides. None by default.