Change the host name

Here is the setup:  Two servers.  Both 2003 using IIS 6.0.  One server is the www.mysite.com (192.168.1.13) server and the DNS server.  Server two is (needs to be) admin.mysite.com (192.168.1.39).  Both servers have internet access and I have added an A record to the DNS server to point all internal traffic asking for admin.mysite.com to the 192.168.100.39 server.

The admin.mysite.com server has several other sits on it currently.  I can only get to them by using http://192.168.100.39/{site name}.  I would like to fix that but it is secondary.

How do I change the hostname in IIS to respond to admin.mysite.com?  Are there DNS issues I will have to address?  I know I created an A record for the internal address, do I do the same for the external address?


Thanks!