Branding is not always necessary in a market that is an oligopoly. However, branding can be essential in many oligopolies.
A firm in an oligopoly can sell a differentiated product or it can sell a homogeneous product. In cases where the market is selling a homogeneous product, branding will not be important. For example, Saudi Arabia will not go to any great lengths to try to "brand" their crude oil. It would do them no real good because crude oil is a relatively homogeneous product.
In cases where the product is differentiated, however, branding is very important. For example, the market for automobiles is an oligopoly. In that market, it is very important for a firm to build its brand. The brand tends to develop a reputation and a relatively faithful customer base.
So, branding is not necessary in all oligopolies because some oligopolistic markets sell homogeneous products. When the product sold is differentiated, though, branding becomes vital.