diff --git a/packages/aws-cdk-lib/core/lib/stack.ts b/packages/aws-cdk-lib/core/lib/stack.ts
index a31610fdfa00c..4d51504a48cc9 100644
--- a/packages/aws-cdk-lib/core/lib/stack.ts
+++ b/packages/aws-cdk-lib/core/lib/stack.ts
@@ -473,7 +473,7 @@ export class Stack extends Construct implements ITaggable {
 
     this._notificationArns = props.notificationArns ?? [];
 
-    if (!VALID_STACK_NAME_REGEX.test(this.stackName)) {
+    if (!Token.isUnresolved(this._stackName) && !VALID_STACK_NAME_REGEX.test(this.stackName)) {
       throw new Error(`Stack name must match the regular expression: ${VALID_STACK_NAME_REGEX.toString()}, got '${this.stackName}'`);
     }
 
diff --git a/packages/aws-cdk-lib/core/test/stack.test.ts b/packages/aws-cdk-lib/core/test/stack.test.ts
index 0f67d1ad6ac7b..77a83ba152919 100644
--- a/packages/aws-cdk-lib/core/test/stack.test.ts
+++ b/packages/aws-cdk-lib/core/test/stack.test.ts
@@ -38,6 +38,19 @@ describe('stack', () => {
     }).toThrow(`Stack name must be <= 128 characters. Stack name: '${reallyLongStackName}'`);
   });
 
+  test('stack name can be a tokenized value', () => {
+    // GIVEN
+    const app = new App({});
+    const stackName = Lazy.string({ produce: () => 'my-dynamic-string' });
+
+    // THEN
+    expect(() => {
+      new Stack(app, 'MyStack', {
+        stackName: stackName,
+      });
+    }).not.toThrow();
+  });
+
   test('stack objects have some template-level propeties, such as Description, Version, Transform', () => {
     const stack = new Stack();
     stack.templateOptions.templateFormatVersion = 'MyTemplateVersion';