Well what are you talking about???
are you talking about an in-house web/mail/DNS server???
If you want to set up a domain at your home/office.. than no you don't need to purchase a domain name.. goofball...
the only reason to purchase a domain name is if you are going to host your own internet based website... i.e. www.yourname.com
To do this you need to have a static IP address... These can be obtained from you internet provider for a fee..
When you purchase the domain name, you will tell then what the IP address is... (you static, external IP address)
Then, if you have a router.. you need to configure port forwarding on your router to forward all access of port 80 to the internal ip address of the webserver.. i.e. 192.168.0.1 or something of that nature..
Tada! You gotchoself a website... lol.. like my word?