Reputation is how you are perceived. Therefore, the perception may be managed and that is why companies invest in corporate branding or even employer branding so that they can be the employer of choice considering today’s war on talents. Legitimacy refers to whether the company follows the social or cultural norms that makes it legitimate business. There are standards that need to be followed to be considered legitimate.
While reputation and legitimacy are similar in many ways, they are not the same. Reputation is more focused on how an entity is perceived in terms of its past actions and track record, while legitimacy often pertains to whether an entity's actions align with societal norms, values, and expectations, and whether it has the right to operate in a certain context. An entity can have a strong reputation but lack legitimacy, or vice versa. Nonetheless, these concepts are closely intertwined and often mutually reinforcing in practice.