diff --git a/packages/type-utils/src/typeOrValueSpecifiers/specifierNameMatches.ts b/packages/type-utils/src/typeOrValueSpecifiers/specifierNameMatches.ts
index 97e7813c6a3a..ac7000f11acb 100644
--- a/packages/type-utils/src/typeOrValueSpecifiers/specifierNameMatches.ts
+++ b/packages/type-utils/src/typeOrValueSpecifiers/specifierNameMatches.ts
@@ -1,18 +1,26 @@
+import * as tsutils from 'ts-api-utils';
 import type * as ts from 'typescript';
 
 export function specifierNameMatches(
   type: ts.Type,
-  name: string[] | string,
+  names: string[] | string,
 ): boolean {
-  if (typeof name === 'string') {
-    name = [name];
+  if (typeof names === 'string') {
+    names = [names];
   }
-  if (name.some(item => item === type.intrinsicName)) {
+
+  const symbol = type.aliasSymbol ?? type.getSymbol();
+  const candidateNames = symbol
+    ? [symbol.escapedName as string, type.intrinsicName]
+    : [type.intrinsicName];
+
+  if (names.some(item => candidateNames.includes(item))) {
     return true;
   }
-  const symbol = type.aliasSymbol ?? type.getSymbol();
-  if (symbol === undefined) {
-    return false;
+
+  if (tsutils.isIntersectionType(type)) {
+    return type.types.some(subType => specifierNameMatches(subType, names));
   }
-  return name.some(item => (item as ts.__String) === symbol.escapedName);
+
+  return false;
 }
diff --git a/packages/type-utils/tests/TypeOrValueSpecifier.test.ts b/packages/type-utils/tests/TypeOrValueSpecifier.test.ts
index fa85b93d0cdb..e2bc32acc2e5 100644
--- a/packages/type-utils/tests/TypeOrValueSpecifier.test.ts
+++ b/packages/type-utils/tests/TypeOrValueSpecifier.test.ts
@@ -369,6 +369,42 @@ describe('TypeOrValueSpecifier', () => {
       ],
     ])('matches a matching package specifier: %s', runTestPositive);
 
+    it.each<[string, TypeOrValueSpecifier]>([
+      [
+        `
+          type Other = { __otherBrand: true };
+          type SafePromise = Promise<number> & { __safeBrand: string };
+          type JoinedPromise = SafePromise & {};
+        `,
+        { from: 'file', name: ['Other'] },
+      ],
+      // The SafePromise alias acts as an actual alias ("cut-and-paste"). I.e.:
+      // type JoinedPromise = Promise<number> & { __safeBrand: string };
+      [
+        `
+          type SafePromise = Promise<number> & { __safeBrand: string };
+          type JoinedPromise = SafePromise & {};
+        `,
+        { from: 'file', name: ['SafePromise'] },
+      ],
+    ])(
+      "doesn't match a mismatched type specifier for an intersection type: %s",
+      runTestNegative,
+    );
+
+    it.each<[string, TypeOrValueSpecifier]>([
+      [
+        `
+          type SafePromise = Promise<number> & { __safeBrand: string };
+          type JoinedPromise = SafePromise & {};
+        `,
+        { from: 'file', name: ['JoinedPromise'] },
+      ],
+    ])(
+      'matches a matching type specifier for an intersection type: %s',
+      runTestPositive,
+    );
+
     it("does not match a `declare global` with the 'global' package name", () => {
       runTestNegative(
         `