While the MONTERO music video (directed by Ukranian director Tanu Muino) is littered with classical imagery, the most prominent reference is the Greek quote from Plato's Symposium (191a) inscribed on the Tree of Life: ἐπειδὴ οὖν ἡ φύσις δίχα ἐτμήθη, ποθοῦν ἕκαστον τὸ ἥμισυ τὸ αὑτοῦ (“when the nature was cut in two, ...

In the context of the story, there's a profound symbolism behind the exchange of names between the two main characters, Elio and Oliver. It becomes a romantic gesture of deep intimacy and vulnerability. Essentially, by calling someone by your own name, you're recognizing them as an extension of yourself.