Under "Desired Output", the T-SQL going to the server becomes:

SELECT '@@servername' AS worked

Putting single-quotes around @@servername makes it a string literal and will not be replaced with the actual name, which is why you are seeing @@servername as the value.

If you're looking to display the server name, remove the single-quotes, making your T-SQL:

SELECT @@servername AS worked

I'm not entirely clear I understand the question, but this is how you would get what's in your "Desired Output".

Under "Desired Output", the T-SQL going to the server becomes:

SELECT '@@servername' AS worked

Putting single-quotes around @@servername makes it a string literal and will not be replaced with the actual name, which is why you are seeing @@servername as the value.

If you're looking to display the server name, remove the single-quotes, making your T-SQL:

SELECT @@servername AS worked

I'm not entirely clear I understand the question, but this is how you would get what's in your "Desired Output".