It is called subcutaneous layer or subcutis (you can find this name in the attached picture). The hypodermis is derived from the mesoderm. In arthropods, the hypodermis emits the chitinous cuticle. The term also refers to a layer of cells lying below the epidermis of plants.
A layer of tissue lies immediately below the dermis of vertebrate skin. It is often called as subcutaneous tissue. It has got larger blood vessels and nerves than those found in the dermis.