fix(eks): eks cluster name exceeding the limit of 100 characters (#34449)

### Issue # (if applicable)

Relates to #30632 but does not close the issue.

### Reason for this change

The cluster name can exceed 100 characters, which exceeds the limit for EKS.

### Description of changes

- Check if the cluster name exceeds 100 characters
- If it does, throw a validation error

### Describe any new or updated permissions being added

N/A

### Description of how you validated changes

Added unit test

### Checklist
- [ ] My code adheres to the [CONTRIBUTING GUIDE](https://github.com/aws/aws-cdk/blob/main/CONTRIBUTING.md) and [DESIGN GUIDELINES](https://github.com/aws/aws-cdk/blob/main/docs/DESIGN_GUIDELINES.md)

----

*By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license*

Author: astiwana

packages/aws-cdk-lib/aws-eks/lib/cluster.ts

@@ -1697,6 +1697,11 @@ export class Cluster extends ClusterBase {
       throw new ValidationError('Cannot specify serviceIpv4Cidr with ipFamily equal to IpFamily.IP_V6', this);
     }
 
+    // Check if the cluster name exceeds 100 characters
+    if (!Token.isUnresolved(this.physicalName) && this.physicalName.length > 100) {
+      throw new ValidationError('Cluster name cannot be more than 100 characters', this);
+    }
+
     this.validateRemoteNetworkConfig(props);
 
     this.authenticationMode = props.authenticationMode;

packages/aws-cdk-lib/aws-eks/test/cluster.test.ts

@@ -112,6 +112,19 @@ describe('cluster', () => {
     }).toThrow(/Cannot specify clusterHandlerSecurityGroup without placeClusterHandlerInVpc set to true/);
   });
 
+  test('throws when cluster name exceeds 100 characters', () => {
+    const { stack } = testFixture();
+    const longClusterName = 'X'.repeat(200);
+
+    expect(() => {
+      new eks.Cluster(stack, 'Cluster', {
+        version: CLUSTER_VERSION,
+        clusterName: longClusterName,
+        kubectlLayer: new KubectlV31Layer(stack, 'KubectlLayer'),
+      });
+    }).toThrow(/Cluster name cannot be more than 100 characters/);
+  });
+
   describe('imported Vpc from unparseable list tokens', () => {
     let stack: cdk.Stack;
     let vpc: ec2.IVpc;