I imagine you understand that the people of both lands now called Greece and Turkey are well intermarried. It’s not inaccurate to refer to St Nicholas as a Turk since that’s the current name of the area where he lived.
There was no such country known as Turkey when St. Nicholas lived. Moreover, Nicholas was Greek by birth (and the area of Asia Minor where he was born was Greek).
The term “Turk” didn’t even come into being until the 6th century, 200 years after Nicholas’s death. And, even at that, the people known as Turks were from an area far to the east of where Nicholas was born (in Patara, which was on the SW coast of the Anatolian Peninsula, on the Mediterranean).