fix: use name instead of type (#4506)

Author: adrians5j

packages/pulumi-aws/src/apps/core/cognitoIdentityProviders/configure.ts

@@ -69,19 +69,29 @@ export const configureAdminCognitoFederation = (
         pulumi.interpolate`${userPoolDomain.output.domain}.auth.${region}.amazoncognito.com`
     );
 
-    const providers = [];
+    const idpConfigs: aws.cognito.IdentityProviderArgs[] = [];
+
     for (const idp of config.identityProviders) {
-        providers.push(
-            app.addResource(aws.cognito.IdentityProvider, {
-                name: idp.type,
-                config: getIdpConfig(idp.type, userPool.output.id, idp)
-            })
-        );
+        const config = getIdpConfig(idp.type, userPool.output.id, idp);
+
+        app.addResource(aws.cognito.IdentityProvider, {
+            name: config.providerName.toString(),
+            config
+        });
+
+        idpConfigs.push(config);
     }
 
     appClient.config.supportedIdentityProviders([
         "COGNITO",
-        ...providers.map(p => p.output.providerType)
+        ...idpConfigs.map(config => {
+            // For built-in identity providers, we use the type as the name. Only for OIDC,
+            // we allow the user to provide a custom name, and we only use the type as a fallback.
+            if (config.providerType === "OIDC") {
+                return config.providerName;
+            }
+            return config.providerType;
+        })
     ]);
 
     appClient.config.allowedOauthScopes(["profile", "email", "openid"]);