When the use of family surnames was first required in Turkey (1935) how did families choose their surnames?

Answer 1

I don't know about Turkey, but in Iran they did the same thing at around the same year "1930s" in many ways:

If a man was a carpenter, his last name would be "Mr. Carpenter".

If his name was "masoud" his last name would become "Masoudi"

Or if he was related to a saint or a prophet, he would choose his name for his "surname".

Answer 2

Most of the families choosed their surname according certain
particular features, character attributes, residing areas, even handicaps one had (p.e. parmaksiz - without finger), profession, looks, education, animals, plants etc etc.