How to ssh to servers internally by hostname without domain name?

You can wildcard and use %h in your config

eg

Host *.eng
  Hostname %h.domainname.com

Now when you do ssh foo.eng it will try to connect to foo.eng.domainname.com.

You can add other options to this config as well; eg forcing the username

Host *.eng
  Hostname %h.domainname.com
  User me

Now when you do ssh foo.eng it will try to connect to foo.eng.domainname.com as the user me.

% ssh foo.eng
ssh: Could not resolve hostname foo.eng.domainname.com: Name or service not known

(well, obviously I get an error before it's not a valid hostname for me!)

So now you only need one rule per country.

If you add

search domainname.com

to /etc/resolv.conf, and use hostname.country, ssh (and other network programs, for that matter) will automatically append domainname.com for you¹.

I don't think adding the different country domains to your search path is a good idea because you may get unexpected behavior if two servers in two different countries share the same hostname²

I believe this method is better than changing the ssh configuration because this allows hostname.country to resolve regardless of the program you're using (telnet, VNC,...).

See resolv.conf(5)

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¹ More accurately, it will append domainname.com if it can't resolve hostname.country by itself.

² In such a scenario hostname will resolve to the server in the country whose domain is listed first in the search path.

You could use the CanonicalDomains option in your ssh config.

Adding the following to your ssh config file will make ssh try to append domainname.com to any host that has at most 1 dot in its name :

CanonicalizeHostname yes
CanonicalDomains domainname.com

With this config ssh foo.eng will first try foo.eng.domainname.com, and fallback to foo.eng if the host cannot be found. Likewise, ssh github.com will first try github.com.domainname.com, so if you want to connect to GitHub, your DNS server should not return records for non existing hosts.

The CanonicalizeMaxDots can be used to control how many dots can appear in the hostname before ssh considers it fully qualified and doesn't append domainname.com. it defaults to 1 which should be enough for you given the scheme you currently have, but if you ever get to something like hostname.city.country you would need to increase it.