In chapter 4 of Island of the Blue Dolphins, what did Karna say that weakened her father?

In chapter four, the characters in Island of the Blue Dolphins determine that Karna’s father was weakened enough to be killed by the Aleuts because he had given the captain his real, true, and secret name. In chapter one of the novel, it is explained that the secret name should not be shared lightly:

I was surprised that he gave his real name to a stranger. Everyone in our tribe had two names, the real one which was secret and was seldom used, and one which was common, for if people use your secret name it becomes worn out and loses its magic.

After her father gives the name to the captain of the Aleuts and is killed, Karna and the villagers agree it was because he told the captain his secret name. The secret name is tied to strength, and because her father gave his away, it took away the power he needed to win the battle. Chapter four explains this idea,

My father was dead. The reason for his death, everyone agreed . . . He told Orlov his secret name. No man who used his secret name could be strong in war.

The idea of the secret name and its connection to strength help to explain why Karna’s people are so secretive around others. Her father trades with the Aleuts, and that is tied to the downfall of their tribe to some extent, because they lose the battle against them.