Choosing a custom slug
Slugs are unique per domain, not shared across all of them.
Set a custom slug the same way regardless of which domain you're using - see How to customize a slug. The one domain-specific thing to know: slugs are unique per domain, not globally. The same slug can exist once on golo.to and separately again on each of your own domains, since they don't share one namespace.
Related articles
Adding a custom domain - Type it into Settings - then complete DNS setup and verification.
Connecting a custom domain - Add your domain and verify it with DNS records.
Creating a branded link - Pick your verified domain when creating the link.
DNS setup - One TXT record to prove ownership, one A or CNAME record to route traffic.