Peckerwood is a college-style clothing company featured in Grand Theft Auto V.
Peckerwood appears to produce "college style" clothing, and was set up in 1908, as shown by the company's insignia. A "peckerwood" is a Southern U.S. term for a woodpecker, as well as an ethic slur for a poor white person (white trash). Male pedestrians, usually younger adults, can be found wearing shirts produced by the company. Their alternative logo is a small woodpecker pecking on the elongated "k" in the logo, which is also used by a billboard found in Vinewood that is iconically tilted over and being pecked by a woodpecker. It is inaccessible to the player and plays no role in the storyline whatsoever.
The company is most likely based on American Eagle Outfitters as seen by their marketing to younger consumers and the fact both have a bird in their logos. It may also be based on other brands such as Abercrombie & Fitch.