By default branch provides a random .link domain. If you would like to make it more branded, you can create a subdomain under your DOMAIN and connect with Branch.
In this video, you can see how we have connected
Creating Sub Domain (We use Name.com, you can use your domain name provider interface)
Using DNS Propagator to test
Apply the same in Branch interface.
This is the same method when you want to update AMAZON SNS (Email Setup) with your Domain providers well.