If it's true that teams embody their manager's personality then it's not surprising that organisations reflect their chief executive's characteristics. How an organisation acts in a crisis is often determined by how the chief executive reacts. If the chief executive exudes calm, then the organisation will not rush to action but take time to produce a measured response. The opposite response is where the organisation goes into a frenzy of action, because the message from the top is ‘drop everything and sort this out'. This is then followed by an incessant demand for updates, briefings, and meetings which ends up distracting staff at all levels from the task.
There are lots of words used to describe an individual which could also apply to an organisation. A person can be resilient with the ability to bounce back from setbacks. This is a quality which is very desirable in an organisation. People can be helpful and organisations can be cooperative. Both individuals and organisations are described as competitive - even aggressively so. Some individuals are noted for their creativity and some organisations have a reputation for innovation.