What are the small muscles at the base of hair follicles that cause goosebumps called?

The small muscles at the base of hair follicles that are responsible for causing goosebumps are known as piloerector muscles. These muscles contract in response to various stimuli, such as cold temperatures or emotional reactions like fear, leading to the hair follicles being pulled upright. This contraction causes the hair to stand on end, resulting in the phenomenon commonly referred to as "goosebumps."

Piloerector muscles are a type of smooth muscle rather than skeletal muscle, which is found in the voluntary muscles of the body. Their contraction is an involuntary response, highlighting their role in the autonomic nervous system. This also differentiates them from other types of muscles mentioned in the question; adipose tissue, for instance, does not involve muscle contractions, skeletal muscles are under conscious control, and circular muscles are typically associated with structures like sphincters rather than hair follicles.