Hey @Bergs
When you enable a private endpoint on a resource, a private DNS zone gets created and traffic to the original endpoint gets rejected. That's why you're getting the error above. What you can do is ask your Azure admin to add a CNAME record to privatelink.servicebus.windows.net
private DNS zone. As for the "The remote certificate is invalid according to the validation procedure: RemoteCertificateNameMismatch" issue, it could be an access or configuration issue. If the VPN doesn't have access to the same VNet or the private DNS zone isn't associated with the VNet that would be an issue. It may also be a VNet peering issue as well, just depends on the existing configuration. Or it may be a misconfiguration with the endpoint itself where deleting it and recreating could resolve the issue.
I would verify the network configuration and setup a VM attached to the same VNet and see if you are able to successfully connect. If you are, then you know the issue is with the VPN access. If you aren't, then you know the issue is with the private endpoint. If the issue is with the endpoint and deleting/recreating it doesn't resolve the issue, comment down below.
For a guide for configuring private endpoint with service bus, see Integrate Azure Service Bus with Azure Private Link Service - Azure Service Bus | Microsoft Learn