Yes, you can.
We do not require you to transfer your domain name registration for us to be your web host. You can simply change the nameservers to the ones provided in your welcome email. However, if you would like us to request to be your registrar, AvangardHosting.com can become the registrar for .com, .net, .org, .name, .us, .ca, .co.uk, .biz, .info along with a variety of domain extensions.