While we see Cinna styling Katniss, it's implied that the tributes are given a general "makeover" to enhance their appearance and make them more appealing to the audience. It's likely that Peeta's stylist was someone working within the Capitol's system but not necessarily a prominent figure like Cinna.
The books and movies focus more on the emotional and strategic aspects of the Games, and the stylists are presented as a background element. It's possible that the lack of a specific stylist for Peeta is a deliberate choice to emphasize his down-to-earth and "boy next door" persona, which contrasts with Katniss' more rebellious image.