I am seeking information about this Greek family name. Does anyone know where Greeks of this name originated from?

I am related to one Demetrius Argyrekis (aka Peter Argyros) who arrived in Australia in the 1800's. His family went by the name Harris (sons Harry and Andrew who lived in Melbourne).

One daughter, Mary, was possibly the first Greek child born in Australia. He had other sons: Sidney (Socrates) and George, who lived in Sydney. He had a daughter who married a Greek man, George Thomas(Argyropoulos). She also went by the name Chionas. She died in Sydney in 1945.