Why and how do symbols from the prehistoric time period have an impact on the symbols of today? (Nike, Disney, CocaCola, Hollister, TNA)
I'm not sure there are symbols from the prehistoric time period that have resonance today, but certainly symbols from ancient human history resonate today. Advertising has often used symbols drawn from mythology to establish appeal with wide audiences. The name "Nike" is the name of a Greek Goddess associated with athletic prowess and speed. Advertising imagery of the turn of the century through the 1930s was very illustrative, and ads drew upon art works that depicted figures of mythology and history. Popular modern illustrators like Maxfield Parrish, Alfonse Mucha and N. C. Wyeth utilized many examples from ancient myths in their very popular work, and created any images used in advertising and publishing. In recent years this decorative advertising art from both Europe and America has become very popular, with many Americans purchasing wall prints, calendars, postcards and other reproductions of it to decorate their homes. Much of the subject matter of this art seems unrelated to the products (such as pasta, fruit juice, perfume or liquor) but this seeming lack of connection opens up rich connections and layers the imagery with meaning: for example, an image of the Greek forest god Pan in an advertisement for an alcoholic beverage.
I also want to add that, as the previous editor said, most inspiration for designs that may have been in use in the past, whatever the period, is a symbolic way to promote the mission of the organization.
I found a website that explains the origin of all logos, and I hope it works for you.