If you have a connection to a Database through Entity Framework and you need to switch it to another database (with the exact same structure) you just need to set the Connection.ConnectionString (as seen below).
I had an application where we created a copy of the Master database when setting up a new client.  So using Entity Framework I switched from the master database to the client (depending on what the admin was doing).

using (MasterEntities aEntities = new MasterEntities())
{//Switch db connected to

aEntities.Database.Connection.ConnectionString = aEntities.Database.Connection.ConnectionString.Replace("OldDatabaseName", "NewDatabaseName");

      //Some Query

}