The person who orders a certificate must to be an owner of a domain name which would be secured. A SSL certificate secures single domain name (e.g. you-domain.com), domain name with subdomains (type Wildcard, e.g. a.you-domain.com, b.you-domain.com, c.you-domain.com etc.) or different names (Multi-Domain SSL).
If you buy a certificate, you should create a CSR and paste it into the registration form.