When trying to deploy a Business Rule Engine Policy in BizTalk Server 2013, I was getting the error:
The database “Server:Instance” associated with the deployment driver does not match database “Server2:Instance2” of the during product configuration.


You can run a SQL script like the following (on my machine, there was only one row in the table, so no where clause was needed).

Update adm_group  set RuleEngineDBServerName = 'VM3-NWALTERS'  
select RuleEngineDBServerName,  RuleEngineDBName, * from adm_group 

where VM3-NWALTERS was my machine name. We used a SYSPREP procedure originally to copy a machine and rename it.