HostMonster typically offers a free domain name for the first year when customers purchase a new hosting plan. This promotion is often included in their shared hosting packages, allowing users to register a new domain at no additional cost during the initial registration process. It is important to note that after the first year, customers will be required to pay the standard renewal fee for the domain name if they wish to retain it. Additionally, existing customers who transfer a domain from another registrar may not qualify for this free domain promotion. For the most current information regarding domain name offers and any specific conditions that may apply, it is always recommended to check the official HostMonster website, as promotions and policies may change over time.