The created class is 'partial'!
public partial class Database1Entities1 : DbContext
{
public Database1Entities1()
: base("name=Database1Entities1")
{
}
... and you call it like this:
using (var ctx = new Database1Entities1())
{
#if DEBUG
ctx.Database.Log = Console.Write;
#endif
so, you need only create a partial own class file for original auto-generated class (with same class name!) and add a new constructor with connection string parameter, like Moho's answer before.
After it you able to use parametrized constructor against original. :-)
example:
using (var ctx = new Database1Entities1(myOwnConnectionString))
{
#if DEBUG
ctx.Database.Log = Console.Write;
#endif