Enthusiasm

Prince Calaf does not make the offer to let Turandot discover his name. Rather, he is wanted by the Chinese, and so cannot reveal his name without dying from torture.

There is a character suspicious of Calaf all along, recognizing him.

Turandot is unaware that one could love a slave girl. She is distraught when the slave girl is able to resist torture out of love. She is also moved by the tears of Timur and Calaf.

Turandot: Who gives you such strength?
Liu: His name is Love!

Calaf tells Turandot that if she stops Liu's torture then sets her and Timur free, he will give her his name. Turandot, moved by Liu's devotion and Calaf's selflessness, is about to hand down the order when Liu kills herself to prevent Calaf's death.

Timur to dead Liu: "It is time to rise! It is morning? Why are you still! I order you to rise!"

To the crowd and Turandot: "You will pay! You will pay!" Right then, lightning strikes a statue of a lion and a thunderstorm comes. The crowd falls to their knees and prostrates to the heavens, and Turandot orders that Liu's body be buried in the grave meant for Calaf. She orders all to leave and not look back.
All leave except Calaf and Turandot (Turandot sadly comments that it takes a man of no character to deny a Princess). Turandot tells Calaf to avenge the woman that loves him. She has dreamed of falling to the same fate as her ancestor. Calaf kisses her over and over, saying that he is "killing" the cold-hearted queen. In the end, Calaf reveals his name (and status as a wanted criminal), then tells Turandot to dispose of him as she pleases for he can run no more. The Princess declares her love and finally gives herself to Calaf.

The two arrive at Liu's burial site, where the Princess announces that she now knows Calaf's name: "His name is Love!"