Create a new instance on a SQL server, but I need to use the default DB instance I need to be able to connect to mydb\wrk when I already have everything in mydb and I do not want to change anything other than being able to connect to mydb\wrk.

I can connect to my database with the following connection string 

Provider = SQLOLEDB.1; Password = ****; Persist Security Info = True; 
User ID = sa; Initial Catalog = Master; Data Source = MyDb


I want to use this: 

Provider = SQLOLEDB.1; Password = ****; Persist Security Info = True; 
User ID = sa; Initial Catalog = Master; Data Source = MyDb\ wrk


I want to change the least possible on the server
There is no need to install an extra instance if you want to connect to the default instance using an instance name.

You can create an alias for that.

Open SQL Server configuration manager on the client machine , and under SQL Server native client configuration for both the 32 and 64 bit node add an alias like this:





And then you can connect using your alias name: