I posted about this previously, but I wanted to post the steps I used to actually rename the server.

• Open BizTalk Server Configuration and Unconfigure all features
• Exit the BizTalk Server Configuration
• Open SQL Server Management Studio and connect to the server
• Expand your server in the Object Explorer and expand the Notification Services node
• Right click on the BAMAlerts instance and select Disable
• Right click on the BAMAlerts instance and select Stop
• Right click on the BAMAlerts instance, point to Tasks, and then select Unregister
  
• Right click on the BAMAlerts instance, point to Tasks, and then select Delete
• In the Object Explorer click on the Databases node
• In the Summary tab on the right of the screen, highlight all databases (do not highlight System Databases or Database Snapshots)
  
• Right click on the highlighted databases and select “Delete”
• The Delete Objects screen will appear, as shown below. Ensure the options are selected as shown in this screenshot, and click OK
  
  • If you receive any errors while deleting databases, expand the Management – Activity Monitor option under your SQL server in Object Explorer and kill any processes running against the database you’re trying to delete
• In Object Explorer, expand Security – Logins and delete all logins used by the previously deleted databases
• Close the SQL Server Management Studio
• Change computer name
• Restart and log in (ignore any failed service startup messages)
• Open SQL Server Management Studio and connect to server using new computer name assigned above
• Open a New Query Window (click the New Query button in the toolbar)
• Enter the following commands, replacing <old_name> and <new_name> with the old and new computer names, respectively
  sp_dropserver ‘<old_name>’
  GO
  sp_addserver ‘<new_name>’, ‘local’
  GO
• Execute the commands by clicking the “Execute” button in the toolbar or hitting F5 on your keyboard
  • If you receive any errors during the sp_dropserver command, execute sp_helpserver and copy the value of network_name for the <old_name> server and paste it into your sp_dropserver parameter, including any spaces
• Restart SQL Server (Right-click on your server under the Object Explorer and select “Restart”), ignoring any errors that appear
• Open Internet Information Services (IIS) from the Start menu
  • Expand Web Sites, Default Web Site and delete the BAM application (if it’s not there, move on to the next step)
  • Expand Application Pools and delete the BAMAppPool (if it’s not there, move on to the next step)
• Open BizTalk Server Configuration from the Start menu
• Perform a Basic Configuration using your new computer name as the Database server name and a current local account as the username for the service credential
  • When the configuration is complete review the results to ensure all features were successfully configured. If any failed, there will be a red “X” next to the failed feature.
  • Any failed features will need to be manually configured, so ensure the option to launch the custom configuration is checked before closing the wizard
  • For each failed feature, click on the option in the left pane of the configuration screen and configure the options in the right pane. Usually, the configuration involves setting a username and password for a service.
• Once the configuration is complete, export the configuration and save the file
• Open BizTalk 2006 Administration Console
  • Expand BizTalk Server 2006 Administration and right-click on the BizTalk Group for <old_name> and select Remove (If the BizTalk Group shown is already using your new computer name skip this step)
  • Right-click on BizTalk Server 2006 Administration and select “Connect to Existing Group”
  • Select your new SQL Server
  • Select the database (BizTalkMgmtDb)
  • Click OK
• Restart the machine

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