diff --git a/demo/markdownlint-browser.js b/demo/markdownlint-browser.js
index 12de7389..074a137d 100644
--- a/demo/markdownlint-browser.js
+++ b/demo/markdownlint-browser.js
@@ -4601,7 +4601,8 @@ module.exports = [
 
 const { addError, escapeForRegExp, filterTokens, forEachInlineChild, forEachHeading, htmlElementRe } = __webpack_require__(/*! ../helpers */ "../helpers/helpers.js");
 // Regular expression for identifying HTML anchor names
-const identifierRe = /(?:id|name)\s*=\s*['"]?([^'"\s>]+)/iu;
+const idRe = /\sid\s*=\s*['"]?([^'"\s>]+)/iu;
+const nameRe = /\sname\s*=\s*['"]?([^'"\s>]+)/iu;
 /**
  * Converts a Markdown heading into an HTML fragment according to the rules
  * used by GitHub.
@@ -4643,11 +4644,10 @@ module.exports = {
             let match = null;
             while ((match = htmlElementRe.exec(token.content)) !== null) {
                 const [tag, , element] = match;
-                if (element.toLowerCase() === "a") {
-                    const idMatch = identifierRe.exec(tag);
-                    if (idMatch) {
-                        fragments.set(`#${idMatch[1]}`, 0);
-                    }
+                const anchorMatch = idRe.exec(tag) ||
+                    (element.toLowerCase() === "a" && nameRe.exec(tag));
+                if (anchorMatch) {
+                    fragments.set(`#${anchorMatch[1]}`, 0);
                 }
             }
         };
diff --git a/lib/md051.js b/lib/md051.js
index 478f3613..b8b67f5a 100644
--- a/lib/md051.js
+++ b/lib/md051.js
@@ -6,7 +6,8 @@ const { addError, escapeForRegExp, filterTokens, forEachInlineChild,
   forEachHeading, htmlElementRe } = require("../helpers");
 
 // Regular expression for identifying HTML anchor names
-const identifierRe = /(?:id|name)\s*=\s*['"]?([^'"\s>]+)/iu;
+const idRe = /\sid\s*=\s*['"]?([^'"\s>]+)/iu;
+const nameRe = /\sname\s*=\s*['"]?([^'"\s>]+)/iu;
 
 /**
  * Converts a Markdown heading into an HTML fragment according to the rules
@@ -55,11 +56,10 @@ module.exports = {
       let match = null;
       while ((match = htmlElementRe.exec(token.content)) !== null) {
         const [ tag, , element ] = match;
-        if (element.toLowerCase() === "a") {
-          const idMatch = identifierRe.exec(tag);
-          if (idMatch) {
-            fragments.set(`#${idMatch[1]}`, 0);
-          }
+        const anchorMatch = idRe.exec(tag) ||
+            (element.toLowerCase() === "a" && nameRe.exec(tag));
+        if (anchorMatch) {
+          fragments.set(`#${anchorMatch[1]}`, 0);
         }
       }
     };
diff --git a/test/link-fragments.md b/test/link-fragments.md
index de9caec4..07221c3e 100644
--- a/test/link-fragments.md
+++ b/test/link-fragments.md
@@ -52,6 +52,10 @@
 
 [Valid](#HREFandID)
 
+[Valid](#id-for-other-element)
+
+[Valid](#id-after-name)
+
 [Valid][goodref]
 
 ### Valid H3 Heading
@@ -125,6 +129,14 @@ Text
 
 <A href="https://example.com" id="HREFandID">Text</A>
 
+<p id="id-for-other-element"></p>
+
+<p name="name-for-other-element"></p>
+
+<input name="name-should-be-ignored" id="id-after-name">
+
+<a data-id="not-an-id-should-be-ignored">
+
 [goodref]: #namedlink
 
 ## Invalid Fragments
@@ -139,6 +151,12 @@ Text
 
 [Invalid](#hrefandid) {MD051}
 
+[Invalid](#name-for-other-element) {MD051}
+
+[Invalid](#name-should-be-ignored) {MD051}
+
+[Invalid](#not-an-id-should-be-ignored) {MD051}
+
 [Invalid][badref] {MD051}
 
 [badref]: #missing
diff --git a/test/snapshots/markdownlint-test-scenarios.js.md b/test/snapshots/markdownlint-test-scenarios.js.md
index cba78172..aed2c4e4 100644
--- a/test/snapshots/markdownlint-test-scenarios.js.md
+++ b/test/snapshots/markdownlint-test-scenarios.js.md
@@ -20950,7 +20950,7 @@ Generated by [AVA](https://avajs.dev).
             31,
           ],
           fixInfo: null,
-          lineNumber: 132,
+          lineNumber: 144,
           ruleDescription: 'Link fragments should be valid',
           ruleInformation: 'https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md051',
           ruleNames: [
@@ -20966,7 +20966,7 @@ Generated by [AVA](https://avajs.dev).
             36,
           ],
           fixInfo: null,
-          lineNumber: 134,
+          lineNumber: 146,
           ruleDescription: 'Link fragments should be valid',
           ruleInformation: 'https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md051',
           ruleNames: [
@@ -20982,7 +20982,7 @@ Generated by [AVA](https://avajs.dev).
             28,
           ],
           fixInfo: null,
-          lineNumber: 136,
+          lineNumber: 148,
           ruleDescription: 'Link fragments should be valid',
           ruleInformation: 'https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md051',
           ruleNames: [
@@ -20998,7 +20998,7 @@ Generated by [AVA](https://avajs.dev).
             18,
           ],
           fixInfo: null,
-          lineNumber: 138,
+          lineNumber: 150,
           ruleDescription: 'Link fragments should be valid',
           ruleInformation: 'https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md051',
           ruleNames: [
@@ -21014,7 +21014,55 @@ Generated by [AVA](https://avajs.dev).
             21,
           ],
           fixInfo: null,
-          lineNumber: 140,
+          lineNumber: 152,
+          ruleDescription: 'Link fragments should be valid',
+          ruleInformation: 'https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md051',
+          ruleNames: [
+            'MD051',
+            'link-fragments',
+          ],
+        },
+        {
+          errorContext: '[Invalid](#name-for-other-element)',
+          errorDetail: null,
+          errorRange: [
+            1,
+            34,
+          ],
+          fixInfo: null,
+          lineNumber: 154,
+          ruleDescription: 'Link fragments should be valid',
+          ruleInformation: 'https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md051',
+          ruleNames: [
+            'MD051',
+            'link-fragments',
+          ],
+        },
+        {
+          errorContext: '[Invalid](#name-should-be-ignored)',
+          errorDetail: null,
+          errorRange: [
+            1,
+            34,
+          ],
+          fixInfo: null,
+          lineNumber: 156,
+          ruleDescription: 'Link fragments should be valid',
+          ruleInformation: 'https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md051',
+          ruleNames: [
+            'MD051',
+            'link-fragments',
+          ],
+        },
+        {
+          errorContext: '[Invalid](#not-an-id-should-be-ignored)',
+          errorDetail: null,
+          errorRange: [
+            1,
+            39,
+          ],
+          fixInfo: null,
+          lineNumber: 158,
           ruleDescription: 'Link fragments should be valid',
           ruleInformation: 'https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md051',
           ruleNames: [
@@ -21027,7 +21075,7 @@ Generated by [AVA](https://avajs.dev).
           errorDetail: null,
           errorRange: null,
           fixInfo: null,
-          lineNumber: 142,
+          lineNumber: 160,
           ruleDescription: 'Link fragments should be valid',
           ruleInformation: 'https://github.com/DavidAnson/markdownlint/blob/v0.0.0/doc/Rules.md#md051',
           ruleNames: [
@@ -21090,6 +21138,10 @@ Generated by [AVA](https://avajs.dev).
       ␊
       [Valid](#HREFandID)␊
       ␊
+      [Valid](#id-for-other-element)␊
+      ␊
+      [Valid](#id-after-name)␊
+      ␊
       [Valid][goodref]␊
       ␊
       ### Valid H3 Heading␊
@@ -21163,6 +21215,14 @@ Generated by [AVA](https://avajs.dev).
       ␊
       <A href="https://example.com" id="HREFandID">Text</A>␊
       ␊
+      <p id="id-for-other-element"></p>␊
+      ␊
+      <p name="name-for-other-element"></p>␊
+      ␊
+      <input name="name-should-be-ignored" id="id-after-name">␊
+      ␊
+      <a data-id="not-an-id-should-be-ignored">␊
+      ␊
       [goodref]: #namedlink␊
       ␊
       ## Invalid Fragments␊
@@ -21177,6 +21237,12 @@ Generated by [AVA](https://avajs.dev).
       ␊
       [Invalid](#hrefandid) {MD051}␊
       ␊
+      [Invalid](#name-for-other-element) {MD051}␊
+      ␊
+      [Invalid](#name-should-be-ignored) {MD051}␊
+      ␊
+      [Invalid](#not-an-id-should-be-ignored) {MD051}␊
+      ␊
       [Invalid][badref] {MD051}␊
       ␊
       [badref]: #missing␊
diff --git a/test/snapshots/markdownlint-test-scenarios.js.snap b/test/snapshots/markdownlint-test-scenarios.js.snap
index fda4e967..1b203b7e 100644
Binary files a/test/snapshots/markdownlint-test-scenarios.js.snap and b/test/snapshots/markdownlint-test-scenarios.js.snap differ