If you want to create more than one geodatabase in the same SQL Server instance, you create multiple SQL Server databases, create a geodatabase in each one, and authorize each geodatabase.
The following graphic illustrates that there are two separate databases on one SQL Server instance, and each database contains a complete geodatabase comprised of geodatabase system objects and user data:
The databases can have any unique name that follows SQL Server rules for identifiers and does not start with a number.
You can use the Create Enterprise Geodatabase tool to create additional databases and geodatabases in a SQL Server instance. Since you already designated the geodatabase administrator user when you created the first geodatabase, be sure to use the same password for the geodatabase administrator when you run the tool a second time.
Client connections can be made to one geodatabase at a time. When connected to a geodatabase on a SQL Server instance, you cannot query information from another geodatabase on the SQL Server instance through that same connection.
For instance, you could connect to database1 in ArcGIS Desktop. When you add data to ArcMap through that connection, you cannot view the data in database2. To access the data in database2, you would set up a second database connection from ArcMap to database2.