You'll need to ask your provider whom they resell SSL with. SSL certificates are in the end (no matter where you order the from) issued by a certificate authority. Thawte, GeoTrust, Symantec and so on are examples of certificate authorities. Providers such as your own or NameCheap also resell their certificates, often at a lower price.
As for whether or not you can create an SSL without registering one - yes, you can. However, it won't be recognized by any visitor as a valid SSL certificate, as it would be self-signed.