The snow spirit would need an offering, it is the rules they set if they want to ask for their help. As he listens to the elf talks about the importance of an offering for spirits, Min Soo cuts off his inspiring talks about spirits and asks his name. It was out of nowhere, the Idol is being random as usual.
The elf is being wary of his intention, but it seems the Idol keeps asking him since it would be too annoying to call him an elf without a name.
"I don't care if you're going to give me your fake name" the Idol states what's in his mind. "I need to call with a name rather than calling you an elf, am I right?".
The elf has given some thought nods reluctantly to Min Soo's request. He gives his name, but Min Soo is uncertain whether he's lying or not.