The concept of anonymity plays a crucial role in Light Yagami's actions as Kira in the anime "Death Note." By remaining anonymous, Light is able to carry out his plans without being easily identified or targeted by law enforcement. This allows him to continue his actions of eliminating criminals without fear of immediate retribution, making it easier for him to manipulate the situation to his advantage. Additionally, anonymity helps Light maintain a sense of power and control over others, as they are unable to pinpoint his true identity, adding to the air of mystery and fear surrounding the character of Kira.