What is a brand called that carries the name of the retailer it belongs to, such as Pick n Pay's "No Name" brand?

The correct option is a).

A brand that carries the name of the retailer it belongs to, like Pick n Pay's "No Name" brand, is known as a private brand or private label brand. These brands are owned by the retailer and sold exclusively in their stores.

The final answer is $\boxed{\text{a. private}}$