This is the 3186th most frequent Japanese word.
名乗る
To give one's name; to identify oneself.
Here, '名乗る' means 'to introduce oneself' or 'to declare one's name or identity', often specifying a name or alias.
彼は木村として名乗った。
He identified himself as Kimura.
In this context, '名乗る' conveys 'to step forward or volunteer oneself for a role or task', indicating self-nomination.
その役職に名乗る人がいない。
No one is stepping forward for that position.
Here, '名乗る' is used to mean 'to confess or claim oneself to be something', often implying taking responsibility or admitting to something.