diff --git a/packages/@aws-cdk/aws-iam/lib/role.ts b/packages/@aws-cdk/aws-iam/lib/role.ts
index 7451f68f31736..edf527647e8e9 100644
--- a/packages/@aws-cdk/aws-iam/lib/role.ts
+++ b/packages/@aws-cdk/aws-iam/lib/role.ts
@@ -162,8 +162,25 @@ export interface FromRoleArnOptions {
    * @default false
    */
   readonly addGrantsToResources?: boolean;
+
+  /**
+   * Any policies created by this role will use this value as their ID, if specified.
+   * Specify this if importing the same role in multiple stacks, and granting it
+   * different permissions in at least two stacks. If this is not specified
+   * (or if the same name is specified in more than one stack),
+   * a CloudFormation issue will result in the policy created in whichever stack
+   * is deployed last overwriting the policies created by the others.
+   *
+   * @default 'Policy'
+   */
+  readonly defaultPolicyName?: string;
 }
 
+/**
+ * Options allowing customizing the behavior of {@link Role.fromRoleName}.
+ */
+export interface FromRoleNameOptions extends FromRoleArnOptions { }
+
 /**
  * IAM Role
  *
@@ -206,12 +223,15 @@ export class Role extends Resource implements IRole {
       public readonly roleArn = roleArn;
       public readonly roleName = roleName;
       private readonly attachedPolicies = new AttachedPolicies();
+      private readonly defaultPolicyName?: string;
       private defaultPolicy?: Policy;
 
       constructor(_scope: Construct, _id: string) {
         super(_scope, _id, {
           account: roleAccount,
         });
+
+        this.defaultPolicyName = options.defaultPolicyName;
       }
 
       public addToPolicy(statement: PolicyStatement): boolean {
@@ -220,7 +240,7 @@ export class Role extends Resource implements IRole {
 
       public addToPrincipalPolicy(statement: PolicyStatement): AddToPrincipalPolicyResult {
         if (!this.defaultPolicy) {
-          this.defaultPolicy = new Policy(this, 'Policy');
+          this.defaultPolicy = new Policy(this, this.defaultPolicyName ?? 'Policy');
           this.attachInlinePolicy(this.defaultPolicy);
         }
         this.defaultPolicy.addStatements(statement);
@@ -298,14 +318,19 @@ export class Role extends Resource implements IRole {
    *
    * The imported role is assumed to exist in the same account as the account
    * the scope's containing Stack is being deployed to.
+
+   * @param scope construct scope
+   * @param id construct id
+   * @param roleName the name of the role to import
+   * @param options allow customizing the behavior of the returned role
    */
-  public static fromRoleName(scope: Construct, id: string, roleName: string) {
+  public static fromRoleName(scope: Construct, id: string, roleName: string, options: FromRoleNameOptions = {}) {
     return Role.fromRoleArn(scope, id, Stack.of(scope).formatArn({
       region: '',
       service: 'iam',
       resource: 'role',
       resourceName: roleName,
-    }));
+    }), options);
   }
 
   public readonly grantPrincipal: IPrincipal = this;
diff --git a/packages/@aws-cdk/aws-iam/package.json b/packages/@aws-cdk/aws-iam/package.json
index 3fd900bcba8e8..4e1b23769d375 100644
--- a/packages/@aws-cdk/aws-iam/package.json
+++ b/packages/@aws-cdk/aws-iam/package.json
@@ -109,6 +109,7 @@
   "awslint": {
     "exclude": [
       "from-signature:@aws-cdk/aws-iam.Role.fromRoleArn",
+      "from-signature:@aws-cdk/aws-iam.Role.fromRoleName",
       "from-method:@aws-cdk/aws-iam.AccessKey",
       "construct-interface-extends-iconstruct:@aws-cdk/aws-iam.IManagedPolicy",
       "props-physical-name:@aws-cdk/aws-iam.OpenIdConnectProviderProps",
diff --git a/packages/@aws-cdk/aws-iam/test/role.from-role-arn.test.ts b/packages/@aws-cdk/aws-iam/test/role.from-role-arn.test.ts
index 05a0fdaac4d58..5ccc7a6828d39 100644
--- a/packages/@aws-cdk/aws-iam/test/role.from-role-arn.test.ts
+++ b/packages/@aws-cdk/aws-iam/test/role.from-role-arn.test.ts
@@ -1,6 +1,6 @@
 import { Template } from '@aws-cdk/assertions';
-import { App, Aws, CfnElement, Lazy, Stack } from '@aws-cdk/core';
-import { AnyPrincipal, ArnPrincipal, IRole, Policy, PolicyStatement, Role } from '../lib';
+import { App, Aws, CfnElement, CfnResource, Lazy, Stack } from '@aws-cdk/core';
+import { AnyPrincipal, ArnPrincipal, Grant, IRole, Policy, PolicyStatement, Role } from '../lib';
 
 /* eslint-disable quote-props */
 
@@ -326,6 +326,60 @@ describe('IAM Role.fromRoleArn', () => {
         });
       });
     });
+
+    describe('imported with a user specified default policy name', () => {
+      test('user specified default policy is used when fromRoleArn() creates a default policy', () => {
+        roleStack = new Stack(app, 'RoleStack');
+        new CfnResource(roleStack, 'SomeResource', {
+          type: 'CDK::Test::SomeResource',
+        });
+        importedRole = Role.fromRoleArn(roleStack, 'ImportedRole',
+          `arn:aws:iam::${roleAccount}:role/${roleName}`, { defaultPolicyName: 'UserSpecifiedDefaultPolicy' });
+
+        Grant.addToPrincipal({
+          actions: ['service:DoAThing'],
+          grantee: importedRole,
+          resourceArns: ['*'],
+        });
+
+        Template.fromStack(roleStack).templateMatches({
+          Resources: {
+            ImportedRoleUserSpecifiedDefaultPolicy7CBF6E85: {
+              Type: 'AWS::IAM::Policy',
+              Properties: {
+                PolicyName: 'ImportedRoleUserSpecifiedDefaultPolicy7CBF6E85',
+              },
+            },
+          },
+        });
+      });
+    });
+
+    test('`fromRoleName()` with options matches behavior of `fromRoleArn()`', () => {
+      roleStack = new Stack(app, 'RoleStack');
+      new CfnResource(roleStack, 'SomeResource', {
+        type: 'CDK::Test::SomeResource',
+      });
+      importedRole = Role.fromRoleName(roleStack, 'ImportedRole',
+        `${roleName}`, { defaultPolicyName: 'UserSpecifiedDefaultPolicy' });
+
+      Grant.addToPrincipal({
+        actions: ['service:DoAThing'],
+        grantee: importedRole,
+        resourceArns: ['*'],
+      });
+
+      Template.fromStack(roleStack).templateMatches({
+        Resources: {
+          ImportedRoleUserSpecifiedDefaultPolicy7CBF6E85: {
+            Type: 'AWS::IAM::Policy',
+            Properties: {
+              PolicyName: 'ImportedRoleUserSpecifiedDefaultPolicy7CBF6E85',
+            },
+          },
+        },
+      });
+    });
   });
 
   describe('imported with a dynamic ARN', () => {
@@ -560,7 +614,7 @@ describe('IAM Role.fromRoleArn', () => {
   });
 });
 
-test('Role.fromRoleName', () => {
+test('Role.fromRoleName with no options ', () => {
   const app = new App();
   const stack = new Stack(app, 'Stack', { env: { region: 'asdf', account: '1234' } });
   const role = Role.fromRoleName(stack, 'MyRole', 'MyRole');