Personality is all about the brand.
It's the stated mission, vision and values of the company. But it is also about the attitudes of the employees and how they demonstrate the living brand through everything that they do.
Whilst mission, vision and values have their place I believe that a brand manifesto is a much better document to engage employees as it sets out the what, how and the why.
Think about brands such a Virgin, Red Bull, Chanel, Ferrari, Bic, Starbucks, Amazon and consider what their personality is. It takes time, even for a start-up business, to develop a personality it is proud of. This is only acheived with a clear picture of where you want to be, a good implementation process and continual monitoring and adjustment.