Hola.
El nombre de dominio queda registrado en el host en donde lo compraste, con este puedes cambiarle el DNS o transferirlo a otro host.
Si el servicio es nuevo y te quejas, seguramente te van a rembolsar algo de dinero, habría que fijarse en los términos y condiciones que proporciona el host.
Justamente en los términos y condicones de MochaHost dice:
Cita: Domain name registration/transfer, domain protection, site builder, setup fees (if apply) are not refundable. A $12.00 license fee will be deducted from all canceled accounts that have activated their web builders prior to the account expiration date, including the first 30 days of service. All specials/free optional services need to be redeemed within the first 2 months of the package start date or the upgrade date (including: free domain registration, SSL, static IP, domain ID protection).
7. Refund: Within the first 30 days as a MochaHost.com customer, if for any reason you are not completely satisfied with our hosting services, we will cancel your account and refund your money for your hosting service. During the first 180 days of the service as a client, you can opt out to cancel your account, and regardless of your commitment (1 year, 2 years, 3 years, etc), you will be pro-rated for all unused hosting fees based on our standard monthly package pricing. On refund, for all accounts that have been Upgraded/Downgraded/Changed OS, there will be a $30.00 non-refundable fee for each incident. For Clients with multiple accounts, the starting date is defined as the earliest date that they become a client of MochaHost.com. There is not refund for partially used month after the first 30 days as a client.
The 30 days money back guarantee and 180 Days Risk Free do NOT cover the following:
Traducción: Que los dominios no son reembolsables y que si usted no está satisfecho del servicio, dentro de los 30 días después de haber contratado el servicio cancelan tu cuenta y te devuelven el dinero.
Saludos y muchísimas suerte !!