For most content databases in WSS v3, you can follow these steps to rename the content
database

1. Go to Central Administration > Application Management > Content Databases to
   find the name of the content database your web application is using
2. On your SQL Server, backup this database, then restore it with the new name.
3. In Central Administration > Application Management > Content Databases select
   the web app you want to change then select the content database. Delete the content
   database from the details page.
4. Add a content database from the Content Databases page pointing to the new database
   you created.

I ran into a problem trying this with the Central Administration web application.
I kind of expected this problem, but I think MS should do a better job of warning
you when you go to remove the content database for the Central administration web
site. The problem is that if you use the GUI to remove the content database, you no
longer have access to the gui. To fix this, you must use STSADM from a command line
to add the new content database. Beyond that,I had to run the command line using alternate
credentials because using my credentials, I got an Access Denied error.

Here are the steps I took to rename the Central Administration Web Application

1. Go to Central Administration > Application Management > Content Databases to
   find the name of the content database your web application is using
2. On your SQL Server, backup this database, then restore it with the new name.
3. In Central Administration > Application Management > Content Databases select
   the web app you want to change then select the content database. Delete the content
   database from the details page.
4. After step 3, you will get an error message on the Central Administration GUI and
   you will not be able to get back into it. If you are not logged into the WSS server
   using the credentials you used for database access, then you will need to run your
   command prompt using the correct database credentials. (I don’t know if this is a
   bug, I know there are parameters to pass a databaseuser and databasepassword to the
   STSADM Command, but they don’t work). In my case I ran
1. runas /user:domain~Sharepoint2007 cmd.exe
5. Change to the directory c:program filescommon filesMicrosoft Sharedweb server
   extensions12bin directory and run the command: stsadm -o addcontentdb -url http://servername:42000 -databasename
   Sharepoint_AdminContent -databaseserver databaseservername