hello,
> Session resumption (caching) No (IDs assigned but not
> accepted)
> Session resumption (tickets) No INTOLERANT
>
> Should I change my config to alter these two results (for performance
> OR
> security)? If so, can anyone identify what config options I should
> add/change?
ssl_session_cache might be useful, please read:
http://nginx.org/en/docs/http/configuring_https_servers.html#optimization
>
> Also, is there a way to force the "Server hostname" to be a specific
> FQDN (that we use for this server and website)?
i think you'd need to configure reverse-dns for your site's name to point
to that server's ip, and you must use A-records, not CNAMES; if this
sounds uncommon to you ask your hosting-provider, they should be able to answer
your questions.
cheers,
mex