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..84198cd5a1592 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
@@ -14,6 +14,7 @@ const parameterGroup = new rds.ParameterGroup(stack, 'ParameterGroup', {
   engine: rds.DatabaseInstanceEngine.postgres({ version: rds.PostgresEngineVersion.VER_15_2 }),
   description: 'desc',
   removalPolicy: cdk.RemovalPolicy.DESTROY,
+  name: 'name',
 });
 
 new rds.DatabaseInstance(stack, 'Instance', {
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..14feb1fc4b7e5 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: {