@Vince already answered this in the comments above, but just in case someone else stumbles across this issue here is the documentation link from the latest version of ArcGIS 10.3.x why one should not rename a SQL Server database that contains a geodatabase:
Methods to move a geodatabase in SQL Server
No matter which of the methods you use to move your SQL Server database, you cannot rename the database. When you restore a database, for example, you are given the opportunity to restore it with a different name. Don't do this with a geodatabase; you won't be able to connect to it.
All object names in the geodatabase system tables are fully qualified
with the database name. In addition, many stored procedures use a
three-part naming syntax in their code, which follows the format
"database.owner.object". If the database name changes, you will
not be able to execute these procedures.
Here's some additional explanation from the Esri Australia team regarding how tempting it is to rename a SQL Server geodatabase to a new naming convention when restoring to a new instance, and why it should not be done:
FAQ: Can you rename the ArcSDE geodatabase in SQL Server?