Carving is primarily used for decorating pots by potters from Santa Clara Pueblo, although it has also been seen on pottery from Acoma, San Ildefonso, Mata Ortiz, Laguna and Hopi. Some contemporary pottery also uses "light carving" (or bas relief) as a term to distinguish between the deep carving used on thick body pieces and the sgraffito (etching, scratching) often used on thinner body pieces.
Margaret Tafoya, the pottery matriarch of Santa Clara, is most famous for her carved pieces but many of her descendants have carried on in that tradition and become award-earning potters in their own right.
In Mata Ortiz, Tavo Silveira and his descendants (and students) sometimes use bas relief to accent their surface designs. From what I've seen, Tavo and his son, Jesus Octavio Silveira, along with Tavo's nephews Lazaro and Lucero Ozuna, are the primary practitioners of this design strategy. But in the highly competitive pottery scene in Mata Ortiz, there are likely others that I am missing.
Hand-made pottery is an international thing and shapes, patterns and designs from everywhere now permeate almost everywhere.