"Turk" is just a name. I doubt there was any deep thinking behind it. It sounded cool; a cool name for a gang of hoodlums.
My own headcanon is that when the Department of Administrative Research was first established, Midgar was in the earliest stages of construction, and there was no Shinra Building. Veld therefore set up a temporary office in some rooms above a pub called "The Turks' Head". Still doesn't explain what Turks are doing in the world of FFVII. Maybe they're some sub-species of tonberry?
Oh look here's a historical photo: