Just the default hostname. It won't reveal all of them or any of the IP addresses of that box. secret-freedom-fighter.ice-cream-shop.example.com could have the same IP as example.com and you'd only know example.com
If you've got one cert with a subject alt name for each host, they'd see them all. If you use SNI and they have different certificates, the domains might still be in Certificate Transparency logs. If a wildcard cert is used, that could help to conceal the exact subdomain.
