"Call me by your name and I'll call you by mine."
The quote from which the title comes. In this moment, Elio and Oliver are in bed on the first night they make love. As they begin to consummate their attraction to one another, Oliver suggests that they assume one another's identity. The quote refers to the fact that the desire to love and make love to is also a desire to merge with the loved one, a desire to assume their identity, to become part of them.
"Muscles are firm, not a straight body in these statues. They're all curved, sometimes impossibly curved, and so nonchalant, hence their ageless ambiguity—as if they're daring you to desire them."
As Perlman and Oliver look at slide images of old nude statues from ancient times, Perlman describes them thus. He talks about the fact that the statues are rounded and "impossibly curved," which creates an "ageless ambiguity" that makes them so desirable. He subtly alludes to Oliver's desire for Elio, the fact that he cannot resist loving and desiring the young man's body.
Oliver: Is there anything you don't know?
Elio: I know nothing, Oliver.
Oliver: Well, you seem to know more than anyone else around here.
Elio: Well, if you only knew how little I really know about the things that matter.
Oliver: What things that matter?
Elio: You know what things.
In town, Elio and Oliver flirt after Elio tells him about a statue in the square. Oliver notes how smart Elio is and Oliver tries to tell his desired about how he is having trouble expressing his feelings. Both of them know that they want the other, but they are unable to say it outright.
"I could show you around."
This quote shows us that Elio is attracted to Oliver from the start. Mere moments after Oliver has arrived at the house, Elio offers to be his tour guide. While this is a nice way of being a good host, it also suggests and foreshadows the fact that he wants to spend time with Oliver, that he is attracted to him.
"We rip out so much of ourselves to be cured of things faster than we should that we go bankrupt by the age of thirty and have less to offer each time we start with someone new. But to make yourself feel nothing so as not to feel anything—what a waste!"
Towards the end of the film, Elio goes to his father, and Perlman alludes to the fact that he knows about his son's affair. He urges Elio not to tamp down any of his feelings, "to be cured of things faster than we should," lest he become an unfeeling shell of who he is before it's too late. Perlman tells his son about the importance of expressing his feelings and maintaining a relationship to them.
"People who read are hiders. They hide who they are. People who hide don't always like who they are."
Marzia, Elio's girlfriend, says this to Elio after he gives her a book of poetry. She confesses that she is a reader like him, but also posits this, that readers are sometimes driven to read because they want to hide from the world, because they do not like themselves. In this moment, Marzia is making a personal revelation about herself, but also insinuating that perhaps she knows Elio has something to hide.
"You're too old not to accept people for who they are. What's wrong with them? What's wrong with them? You call them Sonny and Cher behind their backs..."
When Perlman and Mrs. Perlman's friends, Mounier and Isaac, a gay couple, come to visit, Perlman scolds Elio for being dismissive of them. He tells his son that it is rude of him, not to mention unethical, to be so judgmental of the older couple. In this moment, he spots that his son has a homophobic prejudice, and wants to call it out.
Elio: I'm sick, aren't I?
Oliver: I wish everyone was as sick as you.
After Oliver finds the peach into which Elio ejaculated, Elio is a little ashamed, calling himself sick. Oliver is aroused by the action, however, and tells Elio that he likes it by saying that he wishes everyone was "as sick" as him.
"I don't want you to go."
Elio says this to Oliver, weeping, and it is one of the only moments that he is truly vulnerable with his lover. He lets his heart out in this moment, confessing that he wants their summer fling to last longer.
"From the way your dad spoke to me, he made me feel like a part of the family, almost like a son-in-law. You're so lucky! My father would have carted me off to a correctional facility."
Oliver says this to Elio over the phone at the end of the film, after telling him he's getting married in the spring. Elio tells Oliver that his parents know about their affair, and Oliver confesses that he suspected they knew all along, before telling Elio that the Perlmans are much more accepting than his parents ever were.
