Cuerno literally translates to "horn," like one on an animal. However, it has a famous double meaning in Spanish slang.
The idiom "poner los cuernos" (literally "to put the horns on") means to cheat on a romantic partner. In "TU NAME", the singer reveals the reason for the breakup in one line: "Todo por un cuerno" (All because of an infidelity), making this a powerful and essential piece of slang to learn.
If you are looking for a gentle breakup ballad, Fuerza Regida does not have it for you here. "TU NAME" is pure, loud revenge after getting cheated on. The singer finds out his ex was unfaithful—he literally points out it was "Todo por un cuerno" ("All because of an affair/horn")—and instead of sitting around moping, he flips the switch instantly. He tells her "Ya no te topo, ya vete a la fregada" ("I don't mess with you anymore, go to hell") and jumps straight into an over-the-top party lifestyle to prove he is completely unbothered.
He rubs his comeback in her face with zero filter. He brags about taking someone new out on luxury shopping sprees ("Nos fuimos de shopping y le compré todo lo que nunca te compré" / "We went shopping and I bought her everything I never bought you") and running around with a whole list of women: Briana, Juliana, and Tania. The ultimate insult comes in the catchy Spanglish hook, where he claims he is having so much fun living "la vida de artista" ("the artist life") that he cannot even remember who she is: "No te conozco, mami, mami / Se me olvidó tu name" ("I don't know you, mami / I forgot your name"). It is petty, petty fun, but the energy makes it impossible not to sing along.