diff --git a/doc/api/fs.md b/doc/api/fs.md
index cd9632c4ee1..8681d5c6606 100644
--- a/doc/api/fs.md
+++ b/doc/api/fs.md
@@ -861,7 +861,8 @@ added:
 
 > Stability: 1 - Experimental
 
-An alias for `filehandle.close()`.
+Calls `filehandle.close()` and returns a promise that fulfills when the
+filehandle is closed.
 
 ### `fsPromises.access(path[, mode])`
 
@@ -6745,7 +6746,8 @@ added: REPLACEME
 
 > Stability: 1 - Experimental
 
-An alias for `dir.close()`.
+Calls `dir.close()` and returns a promise that fulfills when the
+dir is closed.
 
 #### `dir[Symbol.Dispose]()`
 
@@ -6755,7 +6757,7 @@ added: REPLACEME
 
 > Stability: 1 - Experimental
 
-An alias for `dir.closeSync()`.
+Calls `dir.closeSync()` and returns `undefined`.
 
 ### Class: `fs.Dirent`
 
diff --git a/lib/_http_server.js b/lib/_http_server.js
index 015a4335d93..a7ef03a1ce0 100644
--- a/lib/_http_server.js
+++ b/lib/_http_server.js
@@ -581,7 +581,7 @@ Server.prototype.close = function close() {
 };
 
 Server.prototype[SymbolAsyncDispose] = assignFunctionName(SymbolAsyncDispose, async function() {
-  return promisify(this.close).call(this);
+  await promisify(this.close).call(this);
 });
 
 Server.prototype.closeAllConnections = function closeAllConnections() {
diff --git a/lib/dgram.js b/lib/dgram.js
index 44f4e4298ad..02394161521 100644
--- a/lib/dgram.js
+++ b/lib/dgram.js
@@ -800,7 +800,7 @@ Socket.prototype[SymbolAsyncDispose] = async function() {
   if (!this[kStateSymbol].handle) {
     return;
   }
-  return FunctionPrototypeCall(promisify(this.close), this);
+  await FunctionPrototypeCall(promisify(this.close), this);
 };
 
 
diff --git a/lib/https.js b/lib/https.js
index 69cbf1cf7a2..aaf5d22de66 100644
--- a/lib/https.js
+++ b/lib/https.js
@@ -117,7 +117,7 @@ Server.prototype.close = function close() {
 };
 
 Server.prototype[SymbolAsyncDispose] = async function() {
-  return FunctionPrototypeCall(promisify(this.close), this);
+  await FunctionPrototypeCall(promisify(this.close), this);
 };
 
 /**
diff --git a/lib/internal/fs/dir.js b/lib/internal/fs/dir.js
index 149ec171b50..7cc1477abca 100644
--- a/lib/internal/fs/dir.js
+++ b/lib/internal/fs/dir.js
@@ -21,7 +21,12 @@ const {
 } = require('internal/errors');
 
 const { FSReqCallback } = binding;
-const internalUtil = require('internal/util');
+const {
+  assignFunctionName,
+  promisify,
+  SymbolAsyncDispose,
+  SymbolDispose,
+} = require('internal/util');
 const {
   getDirent,
   getOptions,
@@ -31,10 +36,6 @@ const {
   validateFunction,
   validateUint32,
 } = require('internal/validators');
-const {
-  SymbolAsyncDispose,
-  SymbolDispose,
-} = internalUtil;
 
 class Dir {
   #handle;
@@ -61,9 +62,9 @@ class Dir {
     validateUint32(this.#options.bufferSize, 'options.bufferSize', true);
 
     this.#readPromisified = FunctionPrototypeBind(
-      internalUtil.promisify(this.#readImpl), this, false);
+      promisify(this.#readImpl), this, false);
     this.#closePromisified = FunctionPrototypeBind(
-      internalUtil.promisify(this.close), this);
+      promisify(this.close), this);
   }
 
   get path() {
@@ -306,12 +307,16 @@ ObjectDefineProperties(Dir.prototype, {
   [SymbolDispose]: {
     __proto__: null,
     ...nonEnumerableDescriptor,
-    value: Dir.prototype.closeSync,
+    value: assignFunctionName(SymbolDispose, function() {
+      this.closeSync();
+    }),
   },
   [SymbolAsyncDispose]: {
     __proto__: null,
     ...nonEnumerableDescriptor,
-    value: Dir.prototype.close,
+    value: assignFunctionName(SymbolAsyncDispose, function() {
+      this.close();
+    }),
   },
   [SymbolAsyncIterator]: {
     __proto__: null,
diff --git a/lib/internal/fs/promises.js b/lib/internal/fs/promises.js
index 75926d48bea..80e1aa42a87 100644
--- a/lib/internal/fs/promises.js
+++ b/lib/internal/fs/promises.js
@@ -272,7 +272,7 @@ class FileHandle extends EventEmitter {
   };
 
   async [SymbolAsyncDispose]() {
-    return this.close();
+    await this.close();
   }
 
   /**
diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index b6504eefaf3..c15852ca4f1 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -3342,7 +3342,7 @@ class Http2Server extends NETServer {
   }
 
   async [SymbolAsyncDispose]() {
-    return promisify(super.close).call(this);
+    await promisify(super.close).call(this);
   }
 }
 
diff --git a/lib/internal/readline/interface.js b/lib/internal/readline/interface.js
index 91dfcb641eb..a076799a890 100644
--- a/lib/internal/readline/interface.js
+++ b/lib/internal/readline/interface.js
@@ -47,7 +47,11 @@ const {
   validateString,
   validateUint32,
 } = require('internal/validators');
-const { SymbolDispose, kEmptyObject } = require('internal/util');
+const {
+  assignFunctionName,
+  kEmptyObject,
+  SymbolDispose,
+} = require('internal/util');
 const {
   inspect,
   getStringWidth,
@@ -1370,7 +1374,9 @@ class Interface extends InterfaceConstructor {
     return this[kLineObjectStream];
   }
 }
-Interface.prototype[SymbolDispose] = Interface.prototype.close;
+Interface.prototype[SymbolDispose] = assignFunctionName(SymbolDispose, function() {
+  this.close();
+});
 
 module.exports = {
   Interface,
diff --git a/lib/internal/streams/readable.js b/lib/internal/streams/readable.js
index 3079474b026..d02f595fa32 100644
--- a/lib/internal/streams/readable.js
+++ b/lib/internal/streams/readable.js
@@ -371,13 +371,13 @@ Readable.prototype[EE.captureRejectionSymbol] = function(err) {
   this.destroy(err);
 };
 
-Readable.prototype[SymbolAsyncDispose] = function() {
+Readable.prototype[SymbolAsyncDispose] = async function() {
   let error;
   if (!this.destroyed) {
     error = this.readableEnded ? null : new AbortError();
     this.destroy(error);
   }
-  return new Promise((resolve, reject) => eos(this, (err) => (err && err !== error ? reject(err) : resolve(null))));
+  await new Promise((resolve, reject) => eos(this, (err) => (err && err !== error ? reject(err) : resolve(null))));
 };
 
 // Manually shove something into the read() buffer.
diff --git a/lib/internal/streams/writable.js b/lib/internal/streams/writable.js
index b74b6088201..a3a1a965b00 100644
--- a/lib/internal/streams/writable.js
+++ b/lib/internal/streams/writable.js
@@ -1151,13 +1151,13 @@ Writable.toWeb = function(streamWritable) {
   return lazyWebStreams().newWritableStreamFromStreamWritable(streamWritable);
 };
 
-Writable.prototype[SymbolAsyncDispose] = function() {
+Writable.prototype[SymbolAsyncDispose] = async function() {
   let error;
   if (!this.destroyed) {
     error = this.writableFinished ? null : new AbortError();
     this.destroy(error);
   }
-  return new Promise((resolve, reject) =>
+  await new Promise((resolve, reject) =>
     eos(this, (err) => (err && err.name !== 'AbortError' ? reject(err) : resolve(null))),
   );
 };
diff --git a/lib/net.js b/lib/net.js
index 7cd2e47eb10..8019c5a4be8 100644
--- a/lib/net.js
+++ b/lib/net.js
@@ -2395,7 +2395,7 @@ Server.prototype[SymbolAsyncDispose] = async function() {
   if (!this._handle) {
     return;
   }
-  return FunctionPrototypeCall(promisify(this.close), this);
+  await FunctionPrototypeCall(promisify(this.close), this);
 };
 
 Server.prototype._emitCloseIfDrained = function() {