You can register .ro domains and every Romanian extension (.com.ro, .info.ro, .org.ro, .store.ro and more), plus international ones such as .com, .net, .org, .e...
The www address and the domain without that prefix can have different configurations. One working does not necessarily mean the other is set up correctly.
Check that the active DNS zone contains the records your hosting provider requires for both addresses. Then check that your hosting service accepts both versions and that your HTTPS certificate covers them. If you want one main address, configure the other version to redirect to it. Changing DNS records does not automatically create this redirect. Before making changes, save the existing configuration and avoid deleting records used for email.