It all hinges on DNS. You have to make sure that the DNS name intranet gets resolved to an IP address. I know how to do this only one way: installing my own DHCP and DNS service for the infrastructure. Bonjour-style should work as well, but I have no experience doing it that way.
The operating systems I know of support DNS suffixes, like .local or example.corp. You'll control the DHCP server on your network, correct? Lets assume it will give out addresses like 192.168.13.128, with a 255.255.255.0 network mask and most importantly, it will give out the address of a DNS server that knows how to answer authoritatively over the example.corp zone and it will say to the DHCP clients that their DNS domain is example.corp. Most operating systems will then try to access http://intranet.example.corp if you type http://intranet.
This is how the short-names will work. Onwards to name-based virtual-hosting, like @Iain said. Let's assume your Apache's configuration says:
Listen *:80
NameVirtualHost *:80
I'll assume the Apache server has the 192.168.13.1/24 IP address. I'd put an A record like s01.srv.example.corp. pointing at 192.168.13.1 and a CNAME like intranet.example.corp. pointing at s01.srv.example.corp. and if you need sub-sites I'd put in site.intranet.example.corp. as well, pointing at the full s01.srv DNS name.
Back to the Apache configuration: you'll need to add virtual-hosts like these:
# this matches the NameVirtualHost directive and
# loosely matches the Listen directive; it could also be:
# NameVirtualHost 192.168.13.1:80 and you'd change this below as well
<VirtualHost *:80>
# notice you'll need both of these;
# they must match what's in the browser Location bar
ServerName intranet.example.corp
ServerAlias intranet
# sorry for the Unix-style paths, I avoid Windows a bit
DocumentRoot /var/www/intranet.example.corp
</VirtualHost>
I don't mind expanding on this, if you need help. Please feel free to ask!
