From the given name Φλωρος (Phloros)
"green", from classical Greek χλωρος (chloros)
, or a nickname from the same word in the sense "greenfinch". In some cases it may also be a shortened form of a derivative of this name, such as Phloropoulos
Derived from Greek metaxi
"silk", and most likely referred to a silk merchant or another occupation that dealt with silk.