Mark 7:26

The term Ἑλληνίς (feminine of Ἑλλήνιος) primarily denotes a Greek woman in classical usage, as evidenced in sources such as Euripides (El. 1076) and Menander (Men. 79). However, in later, particularly Christian-era texts, Ἑλληνίς also acquires the meaning of a pagan/gentile/heathen outsider woman, as seen in Julian’s Epistles (Jul. Ep. 112). 

(cf. LSJ, Ἕλλην)

Σύρος (Syros), i.e. ארם (Aram) (cf. Strong's #758  ארם)

The Greek term Σύρος (Syros), used to describe the region of Syria, is believed to be derived from or connected to the name Aram. The ancient Greeks used Σύρος or Συρία to refer to a region that included the lands of the Arameans (ארם), whose name comes from the root ארם (a-r-m), meaning "elevated/exalted" or "high."

Over time, Σύρος (Syros) evolved as the Greek designation for this broader area, encompassing not just the Aramean territories but also surrounding regions, reflecting the Greeks' adaptation of the local names and their own geographical understanding.

Φοινίκη Phoiniké - palm country (cf. Strong's #5403)