No, that is a completely modern construction. The ancient Egyptians themselves wouldn't even be familiar with the ~30 dynasties that we talk about today, because those were invented by a Greek-Egyptian priest in the 3rd century BCE. The labels Old Kingdom, Middle Kingdom, New Kingdom and Late Period have been suggested by Egyptologists because the dynasties within them belong together from an archaeological perspective. Meaning that the Old Kingdom doesn't start with dynasty 0/1 as might be expected, but rather with dynasty 3, which is when the tentative building of pyramids start; it then ends with dynasty 6, when the building of pyramids stop again due to economic changes in Egypt. Likewise, dynasty 11+12 belong together because the architecture is very similar, and they thus form the Middle Kingdom.