diff --git a/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/aws-cdk-rds-instance-with-rds-parameter-group.assets.json b/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/aws-cdk-rds-instance-with-rds-parameter-group.assets.json
index cf9ecfa597261..b2db8913fb2a3 100644
--- a/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/aws-cdk-rds-instance-with-rds-parameter-group.assets.json
+++ b/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/aws-cdk-rds-instance-with-rds-parameter-group.assets.json
@@ -1,7 +1,7 @@
 {
   "version": "36.0.0",
   "files": {
-    "27d09999310ee1193509c78be177319a1946d9d28632d2362b5f6168fd2078f1": {
+    "239d9f5d8cff7634197e9978eaf8133a6904b71cd0f07fbb239f839c7ce32886": {
       "source": {
         "path": "aws-cdk-rds-instance-with-rds-parameter-group.template.json",
         "packaging": "file"
@@ -9,7 +9,7 @@
       "destinations": {
         "current_account-current_region": {
           "bucketName": "cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}",
-          "objectKey": "27d09999310ee1193509c78be177319a1946d9d28632d2362b5f6168fd2078f1.json",
+          "objectKey": "239d9f5d8cff7634197e9978eaf8133a6904b71cd0f07fbb239f839c7ce32886.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/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/aws-cdk-rds-instance-with-rds-parameter-group.template.json b/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/aws-cdk-rds-instance-with-rds-parameter-group.template.json
index 08798fdefb756..4fb3b3c5d1aa0 100644
--- a/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/aws-cdk-rds-instance-with-rds-parameter-group.template.json
+++ b/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/aws-cdk-rds-instance-with-rds-parameter-group.template.json
@@ -394,8 +394,9 @@
   "ParameterGroup5E32DECB": {
    "Type": "AWS::RDS::DBParameterGroup",
    "Properties": {
+    "DBParameterGroupName": "name",
     "Description": "desc",
-    "Family": "postgres15",
+    "Family": "postgres16",
     "Parameters": {}
    },
    "UpdateReplacePolicy": "Delete",
@@ -481,7 +482,7 @@
     },
     "EnableIAMDatabaseAuthentication": true,
     "Engine": "postgres",
-    "EngineVersion": "15.2",
+    "EngineVersion": "16.2",
     "MasterUserPassword": {
      "Fn::Join": [
       "",
diff --git a/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/manifest.json b/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/manifest.json
index bbaf8c75314a2..5ab6b54ad58d9 100644
--- a/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/manifest.json
+++ b/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.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}/27d09999310ee1193509c78be177319a1946d9d28632d2362b5f6168fd2078f1.json",
+        "stackTemplateAssetObjectUrl": "s3://cdk-hnb659fds-assets-${AWS::AccountId}-${AWS::Region}/239d9f5d8cff7634197e9978eaf8133a6904b71cd0f07fbb239f839c7ce32886.json",
         "requiresBootstrapStackVersion": 6,
         "bootstrapStackVersionSsmParameter": "/cdk-bootstrap/hnb659fds/version",
         "additionalDependencies": [
diff --git a/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/tree.json b/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/tree.json
index e2c109b5469fc..9ab09e1f659fd 100644
--- a/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/tree.json
+++ b/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.js.snapshot/tree.json
@@ -661,8 +661,9 @@
                 "attributes": {
                   "aws:cdk:cloudformation:type": "AWS::RDS::DBParameterGroup",
                   "aws:cdk:cloudformation:props": {
+                    "dbParameterGroupName": "name",
                     "description": "desc",
-                    "family": "postgres15",
+                    "family": "postgres16",
                     "parameters": {}
                   }
                 },
@@ -834,7 +835,7 @@
                     },
                     "enableIamDatabaseAuthentication": true,
                     "engine": "postgres",
-                    "engineVersion": "15.2",
+                    "engineVersion": "16.2",
                     "masterUsername": {
                       "Fn::Join": [
                         "",
diff --git a/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.ts b/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.ts
index 141fefb491cc1..83a9caefd940b 100644
--- a/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.ts
+++ b/packages/@aws-cdk-testing/framework-integ/test/aws-rds/test/integ.instance-with-parameter-group.ts
@@ -11,13 +11,14 @@ const stack = new cdk.Stack(app, 'aws-cdk-rds-instance-with-rds-parameter-group'
 const vpc = new ec2.Vpc(stack, 'VPC', { maxAzs: 2, restrictDefaultSecurityGroup: false });
 
 const parameterGroup = new rds.ParameterGroup(stack, 'ParameterGroup', {
-  engine: rds.DatabaseInstanceEngine.postgres({ version: rds.PostgresEngineVersion.VER_15_2 }),
+  engine: rds.DatabaseInstanceEngine.postgres({ version: rds.PostgresEngineVersion.VER_16_2 }),
   description: 'desc',
   removalPolicy: cdk.RemovalPolicy.DESTROY,
+  name: 'name',
 });
 
 new rds.DatabaseInstance(stack, 'Instance', {
-  engine: rds.DatabaseInstanceEngine.postgres({ version: rds.PostgresEngineVersion.VER_15_2 }),
+  engine: rds.DatabaseInstanceEngine.postgres({ version: rds.PostgresEngineVersion.VER_16_2 }),
   vpc,
   multiAz: false,
   publiclyAccessible: true,
diff --git a/packages/aws-cdk-lib/aws-rds/README.md b/packages/aws-cdk-lib/aws-rds/README.md
index f44921d277e47..6fad15b4734b5 100644
--- a/packages/aws-cdk-lib/aws-rds/README.md
+++ b/packages/aws-cdk-lib/aws-rds/README.md
@@ -1078,6 +1078,7 @@ const parameterGroup = new rds.ParameterGroup(this, 'ParameterGroup', {
   engine: rds.DatabaseInstanceEngine.sqlServerEe({
     version: rds.SqlServerEngineVersion.VER_11,
   }),
+  name: 'my-parameter-group',
   parameters: {
     locks: '100',
   },
diff --git a/packages/aws-cdk-lib/aws-rds/lib/parameter-group.ts b/packages/aws-cdk-lib/aws-rds/lib/parameter-group.ts
index c529bc859d401..ef1f43aac56b1 100644
--- a/packages/aws-cdk-lib/aws-rds/lib/parameter-group.ts
+++ b/packages/aws-cdk-lib/aws-rds/lib/parameter-group.ts
@@ -70,6 +70,13 @@ export interface ParameterGroupProps {
    */
   readonly engine: IEngine;
 
+  /**
+   * The name of this parameter group.
+   *
+   * @default - CloudFormation-generated name
+   */
+  readonly name?: string;
+
   /**
    * Description for this parameter group
    *
@@ -126,6 +133,7 @@ export class ParameterGroup extends Resource implements IParameterGroup {
   private readonly family: string;
   private readonly removalPolicy?: RemovalPolicy;
   private readonly description?: string;
+  private readonly name?: string;
 
   private clusterCfnGroup?: CfnDBClusterParameterGroup;
   private instanceCfnGroup?: CfnDBParameterGroup;
@@ -139,6 +147,7 @@ export class ParameterGroup extends Resource implements IParameterGroup {
     }
     this.family = family;
     this.description = props.description;
+    this.name = props.name;
     this.parameters = props.parameters ?? {};
     this.removalPolicy = props.removalPolicy;
   }
@@ -149,6 +158,7 @@ export class ParameterGroup extends Resource implements IParameterGroup {
       this.clusterCfnGroup = new CfnDBClusterParameterGroup(this, id, {
         description: this.description || `Cluster parameter group for ${this.family}`,
         family: this.family,
+        dbClusterParameterGroupName: this.name,
         parameters: Lazy.any({ produce: () => this.parameters }),
       });
     }
@@ -166,6 +176,7 @@ export class ParameterGroup extends Resource implements IParameterGroup {
       this.instanceCfnGroup = new CfnDBParameterGroup(this, id, {
         description: this.description || `Parameter group for ${this.family}`,
         family: this.family,
+        dbParameterGroupName: this.name,
         parameters: Lazy.any({ produce: () => this.parameters }),
       });
     }
diff --git a/packages/aws-cdk-lib/aws-rds/test/parameter-group.test.ts b/packages/aws-cdk-lib/aws-rds/test/parameter-group.test.ts
index cb8ee7adefc4c..a47d76953bd11 100644
--- a/packages/aws-cdk-lib/aws-rds/test/parameter-group.test.ts
+++ b/packages/aws-cdk-lib/aws-rds/test/parameter-group.test.ts
@@ -29,6 +29,7 @@ describe('parameter group', () => {
     const parameterGroup = new ParameterGroup(stack, 'Params', {
       engine: DatabaseClusterEngine.AURORA,
       description: 'desc',
+      name: 'name',
       parameters: {
         key: 'value',
       },
@@ -37,6 +38,7 @@ describe('parameter group', () => {
 
     // THEN
     Template.fromStack(stack).hasResourceProperties('AWS::RDS::DBParameterGroup', {
+      DBParameterGroupName: 'name',
       Description: 'desc',
       Family: 'aurora5.6',
       Parameters: {
@@ -53,6 +55,7 @@ describe('parameter group', () => {
     const parameterGroup = new ParameterGroup(stack, 'Params', {
       engine: DatabaseClusterEngine.AURORA,
       description: 'desc',
+      name: 'name',
       parameters: {
         key: 'value',
       },
@@ -61,6 +64,7 @@ describe('parameter group', () => {
 
     // THEN
     Template.fromStack(stack).hasResourceProperties('AWS::RDS::DBClusterParameterGroup', {
+      DBClusterParameterGroupName: 'name',
       Description: 'desc',
       Family: 'aurora5.6',
       Parameters: {