Anoitecer literally means "to turn into night" or "to darken". While it's related to the common word "noite" (night), the verb form anoitecer is less common and more evocative.
In this song, Paulinho Moska uses it metaphorically to describe how love can fade or lose its vibrancy without a specific spark. He sings, "Pode o amor anoitecer" (Love can turn into night), suggesting that without the "chama que há em ti" (flame that is in you), love can lose its light and become dark, making it a poetic and memorable choice.
Paulinho Moska sings a plea from someone caught between two contradictory wishes: to be free of a memory and to feel it completely. He opens admitting that distance hasn't dulled anything — "O tempo passa e eu não te vejo" [Time passes and I don't see you] — and keeps circling back to the title line, "Que meu nome é saudade de você" [That my name is longing for you], repeating it like a confession he can't stop making.
He asks to be both destroyed and adored in the same breath — "Vem me matar" [Come kill me], "Vem me amar" [Come love me] — because either one would end the not-knowing at the heart of the song: "Tento tanto entender e continuo sem saber" [I try so hard to understand and I still don't know]. The song never resolves; it just returns to that refrain, again and again, which is exactly the point.