diff --git a/packages/eslint-plugin/src/rules/unified-signatures.ts b/packages/eslint-plugin/src/rules/unified-signatures.ts
index c4c7f9bf427..66f783ec1a8 100644
--- a/packages/eslint-plugin/src/rules/unified-signatures.ts
+++ b/packages/eslint-plugin/src/rules/unified-signatures.ts
@@ -535,7 +535,8 @@ export default util.createRule({
 
       // collect overloads
       TSDeclareFunction(node): void {
-        addOverload(node, node.id.name, getExportingNode(node));
+        const exportingNode = getExportingNode(node);
+        addOverload(node, node.id?.name ?? exportingNode?.type, exportingNode);
       },
       TSCallSignatureDeclaration: addOverload,
       TSConstructSignatureDeclaration: addOverload,
diff --git a/packages/eslint-plugin/tests/rules/unified-signatures.test.ts b/packages/eslint-plugin/tests/rules/unified-signatures.test.ts
index c8f9740662d..38a74429af7 100644
--- a/packages/eslint-plugin/tests/rules/unified-signatures.test.ts
+++ b/packages/eslint-plugin/tests/rules/unified-signatures.test.ts
@@ -128,6 +128,14 @@ export interface Foo {
   bar(baz: string): number[];
   bar(): string[];
 }
+`,
+    `
+declare module "foo" {
+  export default function(foo: number): string[];
+}
+`,
+    `
+export default function(foo: number): string[];
 `,
   ],
   invalid: [
@@ -649,5 +657,33 @@ export function foo(line: number, character?: number): number;
         },
       ],
     },
+    {
+      code: `
+declare module "foo" {
+  export default function(foo: number): string[];
+  export default function(foo: number, bar?: string): string[];
+}
+`,
+      errors: [
+        {
+          messageId: 'omittingSingleParameter',
+          line: 4,
+          column: 40,
+        },
+      ],
+    },
+    {
+      code: `
+export default function(foo: number): string[];
+export default function(foo: number, bar?: string): string[];
+`,
+      errors: [
+        {
+          messageId: 'omittingSingleParameter',
+          line: 3,
+          column: 38,
+        },
+      ],
+    },
   ],
 });
diff --git a/packages/typescript-estree/src/ts-estree/ts-estree.ts b/packages/typescript-estree/src/ts-estree/ts-estree.ts
index 10cd0b7e0fb..afda76ead68 100644
--- a/packages/typescript-estree/src/ts-estree/ts-estree.ts
+++ b/packages/typescript-estree/src/ts-estree/ts-estree.ts
@@ -1061,7 +1061,6 @@ export interface TSConstructSignatureDeclaration extends FunctionSignatureBase {
 }
 
 export interface TSDeclareFunction extends FunctionDeclarationBase {
-  id: Identifier;
   type: AST_NODE_TYPES.TSDeclareFunction;
 }