doc: never test for aborts using err.name

Testing the rejected error is not really safe, especially if adopted
for third-party code. This also makes for a smoother transition if
node APIs adopt signal.reason.

Refs: nodejs#40692
Refs: whatwg/dom#1027

doc/api/events.md

@@ -955,7 +955,7 @@ async function foo(emitter, event, signal) {
     await once(emitter, event, { signal });
     console.log('event emitted!');
   } catch (error) {
-    if (error.name === 'AbortError') {
+    if (signal.aborted) {
       console.error('Waiting for the event was canceled!');
     } else {
       console.error('There was an error', error.message);

doc/api/fs.md

@@ -1484,7 +1484,7 @@ setTimeout(() => ac.abort(), 10000);
     for await (const event of watcher)
       console.log(event);
   } catch (err) {
-    if (err.name === 'AbortError')
+    if (signal.aborted)
       return;
     throw err;
   }

doc/api/stream.md

@@ -2357,18 +2357,16 @@ Or using an `AbortSignal` with a readable stream as an async iterable:
 
 ```js
 const controller = new AbortController();
+const { signal } = ac;
 setTimeout(() => controller.abort(), 10_000); // set a timeout
-const stream = addAbortSignal(
-  controller.signal,
-  fs.createReadStream(('object.json'))
-);
+const stream = addAbortSignal(signal, fs.createReadStream(('object.json')));
 (async () => {
   try {
     for await (const chunk of stream) {
       await process(chunk);
     }
   } catch (e) {
-    if (e.name === 'AbortError') {
+    if (signal.aborted) {
       // The operation was cancelled
     } else {
       throw e;

doc/api/timers.md

@@ -263,7 +263,7 @@ const signal = ac.signal;
 setImmediatePromise('foobar', { signal })
   .then(console.log)
   .catch((err) => {
-    if (err.name === 'AbortError')
+    if (signal.aborted)
       console.log('The immediate was aborted');
   });
 
@@ -281,7 +281,7 @@ const signal = ac.signal;
 setTimeoutPromise(1000, 'foobar', { signal })
   .then(console.log)
   .catch((err) => {
-    if (err.name === 'AbortError')
+    if (signal.aborted)
       console.log('The timeout was aborted');
   });