diff --git a/networking/private-cloud-function-from-onprem/README.md b/networking/private-cloud-function-from-onprem/README.md
index cd581a52..43f58f0c 100644
--- a/networking/private-cloud-function-from-onprem/README.md
+++ b/networking/private-cloud-function-from-onprem/README.md
@@ -21,7 +21,7 @@ curl https://YOUR_REGION-YOUR_PROJECT_ID.cloudfunctions.net/YOUR_FUNCTION_NAME
 |---|---|:---: |:---:|:---:|
 | project_id | Project id. | <code title="">string</code> | ✓ |  |
 | *ip_ranges* | IP ranges used for the VPCs. | <code title="object&#40;&#123;&#10;onprem &#61; string&#10;hub    &#61; string&#10;&#125;&#41;">object({...})</code> |  | <code title="&#123;&#10;onprem &#61; &#34;10.0.1.0&#47;24&#34;,&#10;hub    &#61; &#34;10.0.2.0&#47;24&#34;&#10;&#125;">...</code> |
-| *name* | Name used for new resources. | <code title="">string</code> |  | <code title="">psc-onprem</code> |
+| *name* | Name used for new resources. | <code title="">string</code> |  | <code title="">cf-via-psc</code> |
 | *project_create* | If non null, creates project instead of using an existing one. | <code title="object&#40;&#123;&#10;billing_account_id &#61; string&#10;parent             &#61; string&#10;&#125;&#41;">object({...})</code> |  | <code title="">null</code> |
 | *psc_endpoint* | IP used for the Private Service Connect endpoint, it must not overlap with the hub_ip_range. | <code title="">string</code> |  | <code title="">172.16.32.1</code> |
 | *region* | Region where the resources will be created. | <code title="">string</code> |  | <code title="">europe-west1</code> |
diff --git a/networking/private-cloud-function-from-onprem/main.tf b/networking/private-cloud-function-from-onprem/main.tf
index 95954036..dc4cb2f3 100644
--- a/networking/private-cloud-function-from-onprem/main.tf
+++ b/networking/private-cloud-function-from-onprem/main.tf
@@ -52,6 +52,9 @@ module "vpc-onprem" {
       secondary_ip_range = {}
     }
   ]
+  subnet_private_access = {
+    "${var.region}/${var.name}-onprem" = false
+  }
 }
 
 module "firewall-onprem" {
diff --git a/networking/private-cloud-function-from-onprem/variables.tf b/networking/private-cloud-function-from-onprem/variables.tf
index ab5116ff..70355e17 100644
--- a/networking/private-cloud-function-from-onprem/variables.tf
+++ b/networking/private-cloud-function-from-onprem/variables.tf
@@ -29,7 +29,7 @@ variable "ip_ranges" {
 variable "name" {
   description = "Name used for new resources."
   type        = string
-  default     = "psc-onprem"
+  default     = "cf-via-psc"
 }
 
 variable "project_create" {