He named it "Camachin", using the diminutive form of the surname of Spain's national team coach Jose Antonio Camacho, and presented it to the players.
Camacho accepted the good luck token but joked that his name may not bring any benefit.
"That won't save him from anything," he said.
The puppy was bought for $25 after it was seen in a cage by the Spanish TV crew filming a feature in the Ulsan dog-meat market, close to the Spanish team's training camp.
Camacho was diplomatic when asked about the Korean custom of eating dogs when they are five months old.
Cradling the puppy in his arms, he said: "We eat snails. The customs of all foreign countries are sometimes strange."