diff --git a/packages/@aws-cdk/aws-batch-alpha/lib/managed-compute-environment.ts b/packages/@aws-cdk/aws-batch-alpha/lib/managed-compute-environment.ts
index f7ffec746178c..d5474bf0a9bf3 100644
--- a/packages/@aws-cdk/aws-batch-alpha/lib/managed-compute-environment.ts
+++ b/packages/@aws-cdk/aws-batch-alpha/lib/managed-compute-environment.ts
@@ -1088,6 +1088,7 @@ export class FargateComputeEnvironment extends ManagedComputeEnvironmentBase imp
     const { subnetIds } = props.vpc.selectSubnets(props.vpcSubnets);
     const resource = new CfnComputeEnvironment(this, 'Resource', {
       ...baseManagedResourceProperties(this, subnetIds),
+      computeEnvironmentName: props.computeEnvironmentName,
       computeResources: {
         ...baseManagedResourceProperties(this, subnetIds).computeResources as CfnComputeEnvironment.ComputeResourcesProperty,
         type: this.spot ? 'FARGATE_SPOT' : 'FARGATE',
diff --git a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/BatchManagedComputeEnvironmentTestDefaultTestDeployAssertD4528F80.assets.json b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/BatchManagedComputeEnvironmentTestDefaultTestDeployAssertD4528F80.assets.json
index 7cc31fb504dee..c9ff88daa4353 100644
--- a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/BatchManagedComputeEnvironmentTestDefaultTestDeployAssertD4528F80.assets.json
+++ b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/BatchManagedComputeEnvironmentTestDefaultTestDeployAssertD4528F80.assets.json
@@ -1,5 +1,5 @@
 {
-  "version": "31.0.0",
+  "version": "32.0.0",
   "files": {
     "21fbb51d7b23f6a6c262b46a9caee79d744a3ac019fd45422d988b96d44b2a22": {
       "source": {
diff --git a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/batch-stack.assets.json b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/batch-stack.assets.json
index 7a42d47a88c9b..c479e894b1d84 100644
--- a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/batch-stack.assets.json
+++ b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/batch-stack.assets.json
@@ -1,7 +1,7 @@
 {
-  "version": "31.0.0",
+  "version": "32.0.0",
   "files": {
-    "6ebdcdec29ca32bb55c4daa83140fbc6af6c8a2663beb1c1a833a3d4c6ee12c0": {
+    "81f3134124cef368d56ccabda586dbcbef39a78089edd14c9d641cbcb4e0bad2": {
       "source": {
         "path": "batch-stack.template.json",
         "packaging": "file"
@@ -9,7 +9,7 @@
       "destinations": {
         "current_account-current_region": {
           "bucketName": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}",
-          "objectKey": "6ebdcdec29ca32bb55c4daa83140fbc6af6c8a2663beb1c1a833a3d4c6ee12c0.json",
+          "objectKey": "81f3134124cef368d56ccabda586dbcbef39a78089edd14c9d641cbcb4e0bad2.json",
           "assumeRoleArn": "arn:${AWS::Partition}:iam::${AWS::AccountId}:role/cdk-hnb659fds-file-publishing-role-${AWS::AccountId}-${AWS::Region}"
         }
       }
diff --git a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/batch-stack.template.json b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/batch-stack.template.json
index 39f6afe175e92..2e86fbef42d62 100644
--- a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/batch-stack.template.json
+++ b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/batch-stack.template.json
@@ -457,6 +457,7 @@
    "Type": "AWS::Batch::ComputeEnvironment",
    "Properties": {
     "Type": "managed",
+    "ComputeEnvironmentName": "maxPropsFargateCE",
     "ComputeResources": {
      "MaxvCpus": 512,
      "SecurityGroupIds": [
diff --git a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/cdk.out b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/cdk.out
index 7925065efbcc4..f0b901e7c06e5 100644
--- a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/cdk.out
+++ b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/cdk.out
@@ -1 +1 @@
-{"version":"31.0.0"}
\ No newline at end of file
+{"version":"32.0.0"}
\ No newline at end of file
diff --git a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/integ.json b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/integ.json
index 3ba6117ec37bd..acb2eae98de06 100644
--- a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/integ.json
+++ b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/integ.json
@@ -1,5 +1,5 @@
 {
-  "version": "31.0.0",
+  "version": "32.0.0",
   "testCases": {
     "BatchManagedComputeEnvironmentTest/DefaultTest": {
       "stacks": [
diff --git a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/manifest.json b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/manifest.json
index a34d57abde72f..ef7e040db5067 100644
--- a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/manifest.json
+++ b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/manifest.json
@@ -1,5 +1,5 @@
 {
-  "version": "31.0.0",
+  "version": "32.0.0",
   "artifacts": {
     "batch-stack.assets": {
       "type": "cdk:asset-manifest",
@@ -17,7 +17,7 @@
         "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}/6ebdcdec29ca32bb55c4daa83140fbc6af6c8a2663beb1c1a833a3d4c6ee12c0.json",
+        "stackTemplateAssetObjectUrl": "s3://cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}/81f3134124cef368d56ccabda586dbcbef39a78089edd14c9d641cbcb4e0bad2.json",
         "requiresBootstrapStackVersion": 6,
         "bootstrapStackVersionSsmParameter": "/cdk-bootstrap/hnb659fds/version",
         "additionalDependencies": [
@@ -192,7 +192,10 @@
         "/batch-stack/maximalPropsFargate/Resource": [
           {
             "type": "aws:cdk:logicalId",
-            "data": "maximalPropsFargate2D7D8138"
+            "data": "maximalPropsFargate2D7D8138",
+            "trace": [
+              "!!DESTRUCTIVE_CHANGES: WILL_REPLACE"
+            ]
           }
         ],
         "/batch-stack/minimalPropsEc2/SecurityGroup/Resource": [
@@ -312,10 +315,7 @@
         "/batch-stack/taggedCE/Resource": [
           {
             "type": "aws:cdk:logicalId",
-            "data": "taggedCE5029E6F8",
-            "trace": [
-              "!!DESTRUCTIVE_CHANGES: WILL_REPLACE"
-            ]
+            "data": "taggedCE5029E6F8"
           }
         ],
         "/batch-stack/BootstrapVersion": [
diff --git a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/tree.json b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/tree.json
index 8b24aaded4e56..66d6744028e44 100644
--- a/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/tree.json
+++ b/packages/@aws-cdk/aws-batch-alpha/test/integ.managed-compute-environment.js.snapshot/tree.json
@@ -778,6 +778,7 @@
                   "aws:cdk:cloudformation:type": "AWS::Batch::ComputeEnvironment",
                   "aws:cdk:cloudformation:props": {
                     "type": "managed",
+                    "computeEnvironmentName": "maxPropsFargateCE",
                     "computeResources": {
                       "maxvCpus": 512,
                       "type": "FARGATE_SPOT",
diff --git a/packages/@aws-cdk/aws-batch-alpha/test/managed-compute-environment.test.ts b/packages/@aws-cdk/aws-batch-alpha/test/managed-compute-environment.test.ts
index bc8bb7aae6b3c..de649bfe3daee 100644
--- a/packages/@aws-cdk/aws-batch-alpha/test/managed-compute-environment.test.ts
+++ b/packages/@aws-cdk/aws-batch-alpha/test/managed-compute-environment.test.ts
@@ -5,7 +5,7 @@ import { ArnPrincipal, Role, ServicePrincipal } from 'aws-cdk-lib/aws-iam';
 import { Stack, Duration, Tags } from 'aws-cdk-lib';
 import { capitalizePropertyNames } from './utils';
 import * as batch from '../lib';
-import { AllocationStrategy, ManagedEc2EcsComputeEnvironment, ManagedEc2EcsComputeEnvironmentProps, ManagedEc2EksComputeEnvironment, ManagedEc2EksComputeEnvironmentProps } from '../lib';
+import { AllocationStrategy, ManagedEc2EcsComputeEnvironment, ManagedEc2EcsComputeEnvironmentProps, ManagedEc2EksComputeEnvironment, ManagedEc2EksComputeEnvironmentProps, FargateComputeEnvironment } from '../lib';
 import { CfnComputeEnvironmentProps } from 'aws-cdk-lib/aws-batch';
 
 const defaultExpectedEcsProps: CfnComputeEnvironmentProps = {
@@ -910,3 +910,29 @@ describe('ManagedEc2EksComputeEnvironment', () => {
     });
   });
 });
+
+describe('FargateComputeEnvironment', () => {
+  beforeEach(() => {
+    stack = new Stack();
+    vpc = new ec2.Vpc(stack, 'vpc');
+  });
+
+  test('respects name', () => {
+    // WHEN
+    new FargateComputeEnvironment(stack, 'maximalPropsFargate', {
+      vpc,
+      maxvCpus: 512,
+      computeEnvironmentName: 'maxPropsFargateCE',
+      replaceComputeEnvironment: true,
+      spot: true,
+      terminateOnUpdate: true,
+      updateTimeout: Duration.minutes(30),
+      updateToLatestImageVersion: false,
+    });
+
+    // THEN
+    Template.fromStack(stack).hasResourceProperties('AWS::Batch::ComputeEnvironment', {
+      ComputeEnvironmentName: 'maxPropsFargateCE',
+    });
+  });
+});