Final answer:
The centrosome is the cytoskeletal organizing center in animal cells, situated near the nucleus and containing a pair of centrioles.
Step-by-step explanation:
The name of the organizing center of the cytoskeletal component in animal cells, which is sometimes referred to metaphorically as the "control room" for the cytoskeleton, is the centrosome. The centrosome functions as a microtubule-organizing center and is located near the nucleus of the cell. It plays a crucial role during cell division by organizing the mitotic spindle. The centrosome contains a pair of centrioles, and each centriole is a cylinder made up of nine triplets of microtubules that are arranged perpendicularly to each other.