How can one claim a subdomain of oracle.com?
You cannot 'claim' or create a new DNS record under oracle.com, its a private space. Also, what is maybe adding to the confusion is that an instance created in OCI generally gets a FQDN of instancename.subnetname.vcnname.oraclevcn.com - however, this is an internal only address and resolves only within the VCN is was created in. To have this resolve (and be accessible) externally, it needs a public IP, and you would need to create an appropriate DNS record using your own registered domain name and point it to the public IP address.