From this guys site: http://www.mysharepointadventures.com/2012/11/removing-references-to-old-unused-databases-in-sharepoint-2010/

Over time, as you create / remove service applications, there is a tendency for SharePoint to retain a list of databases that are no longer in use but still referenced in the SharePoint Config database. If you try to remove the database on the SQL server without first removing it from SharePoint, you will get an event logged periodically on your SharePoint Web Front End about being unable to find / access the missing database.

Solution

To remove the orphan databases / databases that are no longer in use.

Run SharePoint Management Shell

Run the command

Get-SPDatabase | fl name,id

Locate the database you wish to remove and copy its ID.
Run the command

$db = Get-SPDatabase (id)
$db.Delete()

Now type Get-SPDatabase again, you should see that the database(s) have been removed.

From this guys great Blog! http://blogs.technet.com/b/meamcs/archive/2012/10/23/renaming-sharepoint-2010-search-service-database-name.aspx

In this post I’m planning to walkthrough the practice of changing the SharePoint 2010 Search Service Database names as you might need it in the following scenarios:

• Replacing the Search Service Application Databases Names that Includes GUID’s to a friendlier name.
• The Database Admin in the Organization is planning to change the naming convention of all the Databases names in the Data Center.
• If you are planning to move from one Farm to another that has a different Naming Convention.

You have many options to do this practice as shown in the below figure, but in this post I will walkthrough the preferred steps only to make it simple and clear:

Renaming Property & Crawl DBs using Central Administration:

Verify that the user account that is performing the procedure is a member of the Farm Administrators SharePoint group.

1. In Central Administration, click Application Management.
2. On the Application Management page, click Manage service applications.
3. Click the name of the Search Service Application.
4. On the Search Administration page, click Modify.
5. On the Manage Search Topology page, the following three databases are listed: Administration, Crawl, and Property. You can point to renamed or moved Crawl or Property databases by using this procedure.
6. Click the database that you want to change, and then click Edit Properties.
7. In the Database Server text box, type the new server location if there is one; in the Database Name text box, type the new name for the database; and then click OK.
8. On the Manage Search Topology page, click Apply Topology Changes.

Notes:

• You cannot point to a renamed or moved Search Administration database by using Central Administration.
• It might take several minutes for the changes to take effect.

Renaming Search Service Application Database using PowerShell:

Verify that you meet the following minimum requirements: See Add-SPShellAdmin.

1. On the Start menu, click All Programs.
2. Click Microsoft SharePoint 2010 Products.
3. Click SharePoint 2010 Management Shell.
4. At the Windows PowerShell command prompt, type the following commands:
   1.  
      • Point the Search Administration database to its new name or location.

$searchapp | Set-SPEnterpriseSearchServiceApplication -DatabaseName "<NewDbName>" -DatabaseServer "<NewServerName>" 

Where:

1.  
   1.  
      •  
        • <NewDbName> is the name of the renamed database
      •  
        • <NewServerName> is the new database location
2. Monitor whether the search instances have finished re-provisioning.

Do {write-host -NoNewline .;Sleep 10; $searchInstance = Get-SPEnterpriseSearchServiceInstance -Local} while ($searchInstance.Status -ne "Online")

Additional References:

1. Rename FAST Search for SharePoint 2010 Databases
2. Rename or  Move Service Application
3. Change database (FAST Search Server 2010 for SharePoint)