Yes, you own the complete rights to your domain name when you register it with BlueHost/HostMonster.
You are the rightful owner of the domain name.
That’s why we want our domain name to be registered with a reputable company such as BlueHost or HostMonster, just like we will only deposit our money in a reputable bank.
Can you buy a domain name from Bluehost?
You can transfer the domain’s registration to your Bluehost account, or you can just assign the domain name with your account without transferring the registration. Here you can keep everything on one bill, purchase domains for multiple years, and set up your domains and hosting to automatically renew.
Can I transfer my domain name from GoDaddy to Bluehost?
Pointing the Domain Name to BlueHost
Select “Use a Domain Not Associated with Your Account.” Sign in to your GoDaddy account control panel. Click on “My Accounts,” and then click on “Domains.” Click on the domain you want to transfer.
How do I transfer my domain name to Bluehost?
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How to transfer a domain in to Bluehost – YouTube
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Can I register my domain with one company and host with another?
Yes, it is possible to buy domain only and you can just point your domain to your other hosting provider. But, most hosting company offer domain and also hosting. You definitely can buy a web domain name from one company and host the site on another companies servers or your own.