If you are looking at this article: http://technet.microsoft.com/en-us/library/jj219654.aspxto rename the search service application databases, be aware that the following approach does not work:
To rename the databases by using SQL Server Management Studio
In Management Studio, connect to the source SQL Server instance, and then expand Databases.
Right-click the Search service application database that you want to rename, click Rename, and then type the new name. Repeat this step for each database that you want to rename.
Note: This is not correct for all databases!
This approach only works for the AnalyticsReporting database!
Here it is the trickiest part that is not explained in the article:
If you want to rename the Crawl and Links databases, backup each of these databases and restore them with the new names.
Then you can proceed with the article. Be aware that there are typos with the code snippets provided, as I mention here.
I hope it helps,
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