diff --git a/inc/updater/namespace.php b/inc/updater/namespace.php
index 5fa48c85..752204f4 100644
--- a/inc/updater/namespace.php
+++ b/inc/updater/namespace.php
@@ -22,6 +22,7 @@
  */
 function bootstrap() {
 	add_action( 'init', __NAMESPACE__ . '\\run' );
+	add_filter( 'upgrader_source_selection', __NAMESPACE__ . '\\move_package_during_install', 10, 4 );
 }
 
 /**
@@ -195,3 +196,93 @@ function get_trusted_keys(): array {
 
 	return $recoded_keys;
 }
+
+/**
+ * Move a package to the correctly named directory during installation.
+ *
+ * @param string      $source        Path of $source.
+ * @param string      $remote_source Path of $remote_source.
+ * @param WP_Upgrader $upgrader      An Upgrader object.
+ * @param array       $hook_extra    Array of hook data.
+ * @return string The correct directory path for installation.
+ */
+function move_package_during_install( $source, $remote_source, $upgrader, $hook_extra ): string {
+	global $wp_filesystem;
+
+	if ( isset( $hook_extra['action'] ) && $hook_extra['action'] !== 'install' ) {
+		// Other actions are handled elsewhere.
+		return $source;
+	}
+
+	if ( ! in_array( $hook_extra['type'], [ 'plugin', 'theme' ], true ) ) {
+		// This package type is not supported.
+		return $source;
+	}
+
+	$did = get_did_by_path( $source, $hook_extra['type'] );
+	if ( is_wp_error( $did ) ) {
+		// This isn't a valid FAIR package.
+		return $source;
+	}
+
+	$did_hash = Packages\get_did_hash( $did->get_id() );
+	if ( str_ends_with( $source, "{$did_hash}/" ) ) {
+		// The directory name is already correct.
+		return $source;
+	}
+
+	$new_source = untrailingslashit( $source ) . "-{$did_hash}/";
+	// Core must be able to find the new source directory.
+	$wp_filesystem->move( $source, $new_source, true );
+
+	return $new_source;
+}
+
+/**
+ * Get a package's DID by its path.
+ *
+ * @param string $path The absolute path to the package's directory or main file.
+ * @param string $type The type of package. Allowed types are 'plugin' or 'theme'.
+ * @return DID|WP_Error The DID object on success, WP_Error on failure.
+ */
+function get_did_by_path( $path, $type ) {
+	global $wp_filesystem;
+
+	if ( $type === 'theme' ) {
+		if ( ! str_ends_with( $path, 'style.css' ) ) {
+			$path = trailingslashit( $path ) . 'style.css';
+		}
+
+		$id = get_file_data( $path, [ 'id' => 'Theme ID' ] )['id'];
+		if ( $id ) {
+			return Packages\parse_did( $id );
+		}
+	}
+
+	if ( $type === 'plugin' ) {
+		if ( str_ends_with( $path, '.php' ) ) {
+			$id = get_file_data( $path, [ 'id' => 'Plugin ID' ] )['id'];
+			return Packages\parse_did( $id );
+		}
+
+		$files = $wp_filesystem->dirlist( $path ) ?: false;
+		if ( ! $files ) {
+			// Finding a DID is impossible.
+			return new WP_Error( 'fair.packages.dirlist_failed', __( "The package's file list could not be retrieved.", 'fair' ) );
+		}
+
+		foreach ( $files as $filename => $data ) {
+			if ( $data['type'] !== 'f' || ! str_ends_with( $filename, '.php' ) ) {
+				continue;
+			}
+
+			$filepath = trailingslashit( $path ) . $filename;
+			$id = get_file_data( $filepath, [ 'id' => 'Plugin ID' ] )['id'];
+			if ( $id ) {
+				return Packages\parse_did( $id );
+			}
+		}
+	}
+
+	return new WP_Error( 'fair.packages.none_found', __( 'No FAIR packages were found.', 'fair' ) );
+}