As a Greek surname this is a term for an Anatolian Greek, i.e., one born in Turkey, not in in Greece. I'm not certain, but I think it can be defined more narrowly: an Ethnic Greek whose first language is Turkish, not Greek. There were other Greek communities in Ottoman Turkey who retained the Greek language, Phanariots, etc. The literal meaning of the name appears to be locative, someone from a place called Karaman. Perhaps Karaman in Turkey was a stronghold of this community. Can anyone add to this note, or correct it?