Can I buy a domain name through Bluehost?

yes, to register a new domain name you will need a Bluehost Hosting Account. Once logged in to your Hosting Account, there will be two different ways to register a domain

From the Register Sub-Tab

1. Login to your Bluehost Control Panel.
2. Click the Domains tab.
3. Click on the sub-tab Register.
4. Enter your desired domain name.
5. Click the check button.
6. Click the green cart button to add the domain to your cart.
7. Under your cart on the far right, click next.
8. Review the Registration Settings and click add to cart.
9. Apply payment details, and checkout.

From the Domains Page

1. Login to your Bluehost Control Panel.
2. Click the Domains tab.
3. From the new domain search box to the left, enter your desired domain name in the Find your domain field.
4. Click the get started button.
5. Click the green cart button to add the domain to your cart.
6. Under your cart on the far right, click next.
7. Review the Registration Settings and click add to cart.
8. Apply payment details, and checkout.