There isn't a specific scientific name for a "blue-eyed shag." This is because "shag" is a general term used to describe several species of birds, and eye color is not a distinguishing feature used in scientific classification.

To determine the scientific name, you'd need to be more specific about which type of shag you're referring to. Some common shag species include:

* Australasian shag (Phalacrocorax carbo)

* Spotted shag (Phalacrocorax punctatus)

* New Zealand shag (Phalacrocorax carunculatus)

* Stewart Island shag (Phalacrocorax chalconotus)

If you can provide more information about the shag you're interested in, such as its location or any other distinguishing characteristics, I can help you find the correct scientific name.