So, Greek "Καλώ" and English "call" must have a common etymology. Very interesting.
But is to call somebody to the phone the same expression as calling them on the phone, i.e., καλώ κάποιον στο τηλέφωνο, or do you phrase it differently?
Καλώ in this situation also means calling someone's name
to come to a place.
In this situation
to come and answer / pick up the phone.
Call Costas to come here. Call to Costas.
But we don't really use it like that.
Normally in this case we use the word "φωνάζω" which in english means "shout"
"Φωνάζω τον Κώστα να έρθει στο τηλέφωνο."
"I'm
shouting to Costas to come to the phone."
But φωνάζω is more between family and friends.
More polite would be "Λέω στον Κώστα να έρθει στο τηλέφωνο )
1) So, calling to the phone " Φωνάζω ( λέω) τον Κώστα να ( έρθει ) σηκώσει / απαντήσει στο τηλέφωνο."
2) Calling on the phone " Καλώ τον Κώστα στο τηλέφωνο, ή
Κάνω ένα τηλεφώνημα στον Κώστα ".