If you are establishing your online presence via Social Media, everything you tweet or posted in your Facebook wall is open to the public. It is always important that what we say is what we are also doing. So we must be consistent of our personal life with our personal brand.
You cannot simply build a personality online that would represent your personal brand, it is way too dangerous. You should live up with the personality that you have associated with your personal brand. Customers will be discouraged if they buy an expensive product only to find out that it doesn't justify the way it was being advertised.
We can always separate business with our personal life, but the social media requires you to integrate your personal life with your personal brand.