What is the name of the microtubule-organizing center found in animal cells as an identifiable structure present during all phases of the cell cycle? centriole centrosome centromere kinetochore?

The correct answer is centrosome.

The centrosome is the main microtubule organizing centre of the animal cell and it is involved in the regulation of cell-cycle progression. During the mitosis, the centrosome microtubules can interact with the chromosomes to build the mitotic spindle.