diff --git a/src/finalisers/iife.js b/src/finalisers/iife.js
index 2eacc14ddc8..592353f3ac5 100644
--- a/src/finalisers/iife.js
+++ b/src/finalisers/iife.js
@@ -3,23 +3,12 @@ import error from '../utils/error.js';
 import getInteropBlock from './shared/getInteropBlock.js';
 import getExportBlock from './shared/getExportBlock.js';
 import getGlobalNameMaker from './shared/getGlobalNameMaker.js';
-import { property, keypath } from './shared/sanitize.js';
+import { keypath } from './shared/sanitize.js';
 import warnOnBuiltins from './shared/warnOnBuiltins.js';
 import trimEmptyImports from './shared/trimEmptyImports.js';
+import setupNamespace from './shared/setupNamespace.js';
 import { isLegal } from '../utils/identifierHelpers.js';
 
-function setupNamespace ( keypath ) {
-	const parts = keypath.split( '.' );
-
-	parts.pop();
-
-	let acc = 'this';
-
-	return parts
-		.map( part => ( acc += property( part ), `${acc} = ${acc} || {};` ) )
-		.join( '\n' ) + '\n';
-}
-
 const thisProp = name => `this${keypath( name )}`;
 
 export default function iife ( bundle, magicString, { exportMode, indentString, intro, outro }, options ) {
@@ -66,7 +55,7 @@ export default function iife ( bundle, magicString, { exportMode, indentString,
 	}
 
 	if ( isNamespaced ) {
-		wrapperIntro = setupNamespace( name ) + wrapperIntro;
+		wrapperIntro = setupNamespace( name, 'this', false, options.globals ) + wrapperIntro;
 	}
 
 	let wrapperOutro = `\n\n}(${dependencies}));`;
diff --git a/src/finalisers/shared/setupNamespace.js b/src/finalisers/shared/setupNamespace.js
new file mode 100644
index 00000000000..e6107b30eaf
--- /dev/null
+++ b/src/finalisers/shared/setupNamespace.js
@@ -0,0 +1,22 @@
+import { property } from './sanitize.js';
+
+export default function setupNamespace ( name, root, forAssignment, globals ) {
+	const parts = name.split( '.' );
+	if (globals) {
+		parts[0] = (typeof globals === 'function' ? globals( parts[0] ) : globals[ parts[ 0 ] ]) || parts[0];
+	}
+
+	const last = parts.pop();
+
+	let acc = root;
+	if (forAssignment) {
+		return parts
+			.map( part => ( acc += property( part ), `${acc} = ${acc} || {}` ) )
+			.concat( `${acc}${property( last )}` )
+			.join( ', ' );
+	} else {
+		return parts
+			.map( part => ( acc += property( part ), `${acc} = ${acc} || {};` ) )
+			.join( '\n' ) + '\n';
+	}
+}
diff --git a/src/finalisers/umd.js b/src/finalisers/umd.js
index 049ea14c44d..ecf2de20b5c 100644
--- a/src/finalisers/umd.js
+++ b/src/finalisers/umd.js
@@ -7,23 +7,13 @@ import esModuleExport from './shared/esModuleExport.js';
 import { property, keypath } from './shared/sanitize.js';
 import warnOnBuiltins from './shared/warnOnBuiltins.js';
 import trimEmptyImports from './shared/trimEmptyImports.js';
+import setupNamespace from './shared/setupNamespace.js';
 
 function globalProp ( name ) {
 	if ( !name ) return 'null';
 	return `global${ keypath( name ) }`;
 }
 
-function setupNamespace ( name ) {
-	const parts = name.split( '.' );
-	const last = property( parts.pop() );
-
-	let acc = 'global';
-	return parts
-		.map( part => ( acc += property( part ), `${acc} = ${acc} || {}` ) )
-		.concat( `${acc}${last}` )
-		.join( ', ' );
-}
-
 function safeAccess ( name ) {
 	const parts = name.split( '.' );
 
@@ -57,7 +47,7 @@ export default function umd ( bundle, magicString, { exportMode, getPath, indent
 	if ( exportMode === 'named' ) {
 		amdDeps.unshift( `'exports'` );
 		cjsDeps.unshift( `exports` );
-		globalDeps.unshift( `(${setupNamespace(options.name)} = ${options.extend ? `${globalProp(options.name)} || ` : '' }{})` );
+		globalDeps.unshift( `(${setupNamespace(options.name, 'global', true, options.globals)} = ${options.extend ? `${globalProp(options.name)} || ` : '' }{})` );
 
 		args.unshift( 'exports' );
 	}
@@ -71,7 +61,7 @@ export default function umd ( bundle, magicString, { exportMode, getPath, indent
 	const define = amdOptions.define || 'define';
 
 	const cjsExport = exportMode === 'default' ? `module.exports = ` : ``;
-	const defaultExport = exportMode === 'default' ? `${setupNamespace(options.name)} = ` : '';
+	const defaultExport = exportMode === 'default' ? `${setupNamespace(options.name, 'global', true, options.globals)} = ` : '';
 
 	const useStrict = options.strict !== false ? ` 'use strict';` : ``;
 
diff --git a/test/form/samples/use-global-map-for-export-name/_config.js b/test/form/samples/use-global-map-for-export-name/_config.js
new file mode 100644
index 00000000000..1e589caa2fa
--- /dev/null
+++ b/test/form/samples/use-global-map-for-export-name/_config.js
@@ -0,0 +1,10 @@
+module.exports = {
+	description: 'applies globals to output name',
+	options: {
+		name: 'leaflet.terminator',
+		external: [ 'leaflet' ],
+		globals: {
+			'leaflet': 'L'
+		}
+	}
+};
diff --git a/test/form/samples/use-global-map-for-export-name/_expected/amd.js b/test/form/samples/use-global-map-for-export-name/_expected/amd.js
new file mode 100644
index 00000000000..3ee270a88f1
--- /dev/null
+++ b/test/form/samples/use-global-map-for-export-name/_expected/amd.js
@@ -0,0 +1,8 @@
+define(['leaflet'], function (L) { 'use strict';
+
+	L = L && L.hasOwnProperty('default') ? L['default'] : L;
+
+	L.terminator = function(options) {
+	};
+
+});
diff --git a/test/form/samples/use-global-map-for-export-name/_expected/cjs.js b/test/form/samples/use-global-map-for-export-name/_expected/cjs.js
new file mode 100644
index 00000000000..9a71b1060c9
--- /dev/null
+++ b/test/form/samples/use-global-map-for-export-name/_expected/cjs.js
@@ -0,0 +1,8 @@
+'use strict';
+
+function _interopDefault (ex) { return (ex && (typeof ex === 'object') && 'default' in ex) ? ex['default'] : ex; }
+
+var L = _interopDefault(require('leaflet'));
+
+L.terminator = function(options) {
+};
diff --git a/test/form/samples/use-global-map-for-export-name/_expected/es.js b/test/form/samples/use-global-map-for-export-name/_expected/es.js
new file mode 100644
index 00000000000..183aab39a1d
--- /dev/null
+++ b/test/form/samples/use-global-map-for-export-name/_expected/es.js
@@ -0,0 +1,4 @@
+import L from 'leaflet';
+
+L.terminator = function(options) {
+};
diff --git a/test/form/samples/use-global-map-for-export-name/_expected/iife.js b/test/form/samples/use-global-map-for-export-name/_expected/iife.js
new file mode 100644
index 00000000000..5ba1f560aad
--- /dev/null
+++ b/test/form/samples/use-global-map-for-export-name/_expected/iife.js
@@ -0,0 +1,10 @@
+this.L = this.L || {};
+(function (L) {
+	'use strict';
+
+	L = L && L.hasOwnProperty('default') ? L['default'] : L;
+
+	L.terminator = function(options) {
+	};
+
+}(L));
diff --git a/test/form/samples/use-global-map-for-export-name/_expected/umd.js b/test/form/samples/use-global-map-for-export-name/_expected/umd.js
new file mode 100644
index 00000000000..47e48e577f5
--- /dev/null
+++ b/test/form/samples/use-global-map-for-export-name/_expected/umd.js
@@ -0,0 +1,12 @@
+(function (global, factory) {
+	typeof exports === 'object' && typeof module !== 'undefined' ? factory(require('leaflet')) :
+	typeof define === 'function' && define.amd ? define(['leaflet'], factory) :
+	(factory(global.L));
+}(this, (function (L) { 'use strict';
+
+	L = L && L.hasOwnProperty('default') ? L['default'] : L;
+
+	L.terminator = function(options) {
+	};
+
+})));
diff --git a/test/form/samples/use-global-map-for-export-name/main.js b/test/form/samples/use-global-map-for-export-name/main.js
new file mode 100644
index 00000000000..183aab39a1d
--- /dev/null
+++ b/test/form/samples/use-global-map-for-export-name/main.js
@@ -0,0 +1,4 @@
+import L from 'leaflet';
+
+L.terminator = function(options) {
+};