diff --git a/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/integ-provider-with-waiter-state-machine.assets.json b/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/integ-provider-with-waiter-state-machine.assets.json
index 4a22c0ee84968..b616fa67738ed 100644
--- a/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/integ-provider-with-waiter-state-machine.assets.json
+++ b/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/integ-provider-with-waiter-state-machine.assets.json
@@ -27,7 +27,7 @@
         }
       }
     },
-    "c4934037912635137a61ff14a2b2623fa08b180c4b757ad915d6fd9365ffb971": {
+    "f846c7dce86a836c27a5ff81d868b42f46e94502cd6f0859944c4d9e48751e33": {
       "source": {
         "path": "integ-provider-with-waiter-state-machine.template.json",
         "packaging": "file"
@@ -35,7 +35,7 @@
       "destinations": {
         "current_account-current_region": {
           "bucketName": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}",
-          "objectKey": "c4934037912635137a61ff14a2b2623fa08b180c4b757ad915d6fd9365ffb971.json",
+          "objectKey": "f846c7dce86a836c27a5ff81d868b42f46e94502cd6f0859944c4d9e48751e33.json",
           "assumeRoleArn": "arn:${AWS::Partition}:iam::${AWS::AccountId}:role/cdk-hnb659fds-file-publishing-role-${AWS::AccountId}-${AWS::Region}"
         }
       }
diff --git a/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/integ-provider-with-waiter-state-machine.template.json b/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/integ-provider-with-waiter-state-machine.template.json
index ef09953f183a4..f8920f09d9ca3 100644
--- a/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/integ-provider-with-waiter-state-machine.template.json
+++ b/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/integ-provider-with-waiter-state-machine.template.json
@@ -2077,7 +2077,18 @@
   "MyProviderWithDefaultLogwaiterstatemachineLogGroup5907E67B": {
    "Type": "AWS::Logs::LogGroup",
    "Properties": {
-    "LogGroupName": "/aws/vendedlogs/states/waiter-state-machine-c8755c6a4f7af107037ba386c1af047796ca4678a8-Logs",
+    "LogGroupName": {
+     "Fn::Join": [
+      "",
+      [
+       "/aws/vendedlogs/states/waiter-state-machine-",
+       {
+        "Ref": "MyProviderWithDefaultLogframeworkisCompleteC86EC850"
+       },
+       "-c8755c6a4f7af107037ba386c1af047796ca4678a8"
+      ]
+     ]
+    },
     "RetentionInDays": 731
    },
    "UpdateReplacePolicy": "Retain",
diff --git a/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/manifest.json b/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/manifest.json
index c1c67f385b368..ccb36ad429810 100644
--- a/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/manifest.json
+++ b/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/manifest.json
@@ -18,7 +18,7 @@
         "validateOnSynth": false,
         "assumeRoleArn": "arn:${AWS::Partition}:iam::${AWS::AccountId}:role/cdk-hnb659fds-deploy-role-${AWS::AccountId}-${AWS::Region}",
         "cloudFormationExecutionRoleArn": "arn:${AWS::Partition}:iam::${AWS::AccountId}:role/cdk-hnb659fds-cfn-exec-role-${AWS::AccountId}-${AWS::Region}",
-        "stackTemplateAssetObjectUrl": "s3://cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}/c4934037912635137a61ff14a2b2623fa08b180c4b757ad915d6fd9365ffb971.json",
+        "stackTemplateAssetObjectUrl": "s3://cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}/f846c7dce86a836c27a5ff81d868b42f46e94502cd6f0859944c4d9e48751e33.json",
         "requiresBootstrapStackVersion": 6,
         "bootstrapStackVersionSsmParameter": "/cdk-bootstrap/hnb659fds/version",
         "additionalDependencies": [
@@ -391,7 +391,10 @@
         "/integ-provider-with-waiter-state-machine/MyProviderWithDefaultLog/waiter-state-machine/LogGroup/Resource": [
           {
             "type": "aws:cdk:logicalId",
-            "data": "MyProviderWithDefaultLogwaiterstatemachineLogGroup5907E67B"
+            "data": "MyProviderWithDefaultLogwaiterstatemachineLogGroup5907E67B",
+            "trace": [
+              "!!DESTRUCTIVE_CHANGES: WILL_REPLACE"
+            ]
           }
         ],
         "/integ-provider-with-waiter-state-machine/MyProviderWithDefaultLog/waiter-state-machine/Resource": [
diff --git a/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/tree.json b/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/tree.json
index 6d91d1944abdb..da6e395044085 100644
--- a/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/tree.json
+++ b/packages/@aws-cdk-testing/framework-integ/test/custom-resources/test/provider-framework/integ.provider-with-waiter-state-machine.js.snapshot/tree.json
@@ -3006,7 +3006,18 @@
                         "attributes": {
                           "aws:cdk:cloudformation:type": "AWS::Logs::LogGroup",
                           "aws:cdk:cloudformation:props": {
-                            "logGroupName": "/aws/vendedlogs/states/waiter-state-machine-c8755c6a4f7af107037ba386c1af047796ca4678a8-Logs",
+                            "logGroupName": {
+                              "Fn::Join": [
+                                "",
+                                [
+                                  "/aws/vendedlogs/states/waiter-state-machine-",
+                                  {
+                                    "Ref": "MyProviderWithDefaultLogframeworkisCompleteC86EC850"
+                                  },
+                                  "-c8755c6a4f7af107037ba386c1af047796ca4678a8"
+                                ]
+                              ]
+                            },
                             "retentionInDays": 731
                           }
                         },
diff --git a/packages/aws-cdk-lib/custom-resources/lib/provider-framework/waiter-state-machine.ts b/packages/aws-cdk-lib/custom-resources/lib/provider-framework/waiter-state-machine.ts
index 16c251809d8e0..02e5853535760 100644
--- a/packages/aws-cdk-lib/custom-resources/lib/provider-framework/waiter-state-machine.ts
+++ b/packages/aws-cdk-lib/custom-resources/lib/provider-framework/waiter-state-machine.ts
@@ -89,6 +89,7 @@ export class WaiterStateMachine extends Construct {
    * The ARN of the state machine.
    */
   public readonly stateMachineArn: string;
+  private readonly isCompleteHandler: IFunction;
 
   constructor(scope: Construct, id: string, props: WaiterStateMachineProps) {
     super(scope, id);
@@ -125,6 +126,7 @@ export class WaiterStateMachine extends Construct {
       },
     });
 
+    this.isCompleteHandler = props.isCompleteHandler;
     const resource = new CfnStateMachine(this, 'Resource', {
       definitionString: definition,
       roleArn: role.roleArn,
@@ -173,12 +175,9 @@ export class WaiterStateMachine extends Construct {
       resources: ['*'],
     }));
 
-    // Using `node.addr` because it needs to be a unique log group name in the AWS account,
-    // not using `node.path` because of the possibility of exceeding the maximum number of characters for the log group name.
-    // The `addr` value does not change when moving the construct tree using the ID `Default`.
     const logGroupName =
       FeatureFlags.of(this).isEnabled(cxapi.WAITER_STATE_MACHINE_LOG_GROUP_NAME)
-        ? `/aws/vendedlogs/states/waiter-state-machine-${this.node.addr}-Logs`
+        ? `/aws/vendedlogs/states/waiter-state-machine-${this.isCompleteHandler.functionName}-${this.node.addr}`
         : undefined;
     const logGroup = logOptions?.destination ?? new LogGroup(this, 'LogGroup', {
       logGroupName,
diff --git a/packages/aws-cdk-lib/custom-resources/test/provider-framework/waiter-state-machine.test.ts b/packages/aws-cdk-lib/custom-resources/test/provider-framework/waiter-state-machine.test.ts
index 8198f6f074362..11f5f18d0e734 100644
--- a/packages/aws-cdk-lib/custom-resources/test/provider-framework/waiter-state-machine.test.ts
+++ b/packages/aws-cdk-lib/custom-resources/test/provider-framework/waiter-state-machine.test.ts
@@ -292,7 +292,18 @@ describe('state machine', () => {
 
     // THEN
     Template.fromStack(stack).hasResourceProperties('AWS::Logs::LogGroup', {
-      LogGroupName: '/aws/vendedlogs/states/waiter-state-machine-c892b744a2306a661f17f50ce17de4b606ce3fc700-Logs',
+      LogGroupName: {
+        'Fn::Join': [
+          '',
+          [
+            '/aws/vendedlogs/states/waiter-state-machine-',
+            {
+              Ref: 'isCompleteBBB74F92',
+            },
+            '-c892b744a2306a661f17f50ce17de4b606ce3fc700',
+          ],
+        ],
+      },
     });
   });
 });