This feature is available with some paid plans
Auto-branding is the ability to automatically brand links to your website domains, regardless of who creates the link. When someone uses Bitly to shorten a link to one of your websites, the link is automatically created with your custom domain.
Here's a real-life example: If you shorten a link to an Amazon listing, you get a short link using the domain amzn.to instead of bit.ly.
If someone has a custom domain in their Bitly account, they can choose to shorten the link using their own domain, rather than the auto-branded domain.
Auto-branding is available with Enterprise plans only. To activate it, prepare a list of your website domains and talk to your Customer Success Manager.