Resolve hostname without FQDN

I'm trying to configure Bind for internal LAN usage only (Linux server, Windows clients) and I would like to resolve workstation both by fqdn and shortname.
For example, without DNS server, supposing to have a host named host001 I'm able to do:

    nslookup host001
    ping host001

And it works. Using a DNS server I need to specify the FQDN:

    nslookup host001.example.com
    ping host001.example.com

Is there a way to enter a shortname in DNS so writing host001 I obtain the resolve query of host001.example.com?

Thank You

The way I usually see this done is by having the DNS server resolve just the FQDN, but adding the domain to the search list in the DNS config on the clients. You can push this out to the clients via DHCP. I have two networks running in this way and it just works, with no issues on Windows, Linux, or Mac.