When you create your WordPress.com account, you also have a Gravatar URL reserved for you based on your WordPress.com username. For example, If your username is my-groovy-username, your Gravatar profile is reserved at https://gravatar.com/my-groovy-username.
Now you can register one custom .link domain for your Gravatar profile at no cost for one year – this is a limited-time offer. That means that in addition to your profile being located at https://gravatar.com/my-groovy-username, it would also be reached at a custom, memorable domain like https://my-groovy-username.link.
You can get a custom .link domain by logging in to your Gravatar profile and clicking the “Claim domain” link in the left sidebar:

You are then taken to WordPress.com to choose your domain name:

After you choose your domain, you’re taken to the checkout page:

When you complete checkout, you can return to Gravatar:

After a few minutes, your domain will be active, and you should receive an email to say your domain is now active:

If you visit your new .link domain address, you should reach your Gravatar profile.
This custom .link domain is free for one year. If you want to keep it after one year, you can renew your domain for the standard domain renewal fee. Your domain includes a free SSL certificate.
You can have only one domain for your Gravatar profile. While your custom domain is being used for your Gravatar profile, you’ll be able to do only specific actions with it:
Other features, such as managing DNS, changing name servers, or adding email will not be accessible while the domain is being used in Gravatar. If you want to have complete control over your domain, you can transfer it to another registrar. However, keep in mind that if you transfer your domain away or delete it and, in the future, you want to add another domain to your Gravatar profile, you will have to pay the standard fee to register it.