Final answer:
The blotchy, brownish coloring that the pregnant client is experiencing is called melasma, which is a common integumentary change due to hormonal changes in pregnancy.
Step-by-step explanation:
The correct term for the blotchy, brownish coloring over the cheeks, nose, and forehead that the pregnant client is experiencing is known as melasma. This skin condition is related to hormonal changes during pregnancy, specifically an increase in melanocyte-stimulating hormone in conjunction with estrogens. These hormonal changes can lead to increased melanin production, which in turn can cause the darkening or discoloration of the skin on the face, also referred to as the "mask of pregnancy" or chloasma.