default domain name

I am trying out the proxy (without cache module) functionality in nginx.

Here is the problem I am encountering
On the client machine the default domain name is company.com
when user types in http://department in the browser, the DNS resolves to department.company.com
When this http request gets intercepted by the nginx proxy, it is not able to process the request. It gives an error "cannot resolve department"

tcpdump trace showed that the http request has the HOST header without the domain name.
HOST: department

Is there any way we can specify a default domain name in nginx config.

From further investigating found that the server_name directive matches the HOST header. Is there any rewrite regex we could use
such that IF the HOST header has a value without domain name THEN add the default domain name.