The transmembrane domain of an integral membrane protein is called

hydrophobic core or membrane spanning domain

Explanation:

Integral Membrane Proteins:

Integral membrane proteins are a type of membrane protein that possess segments that are embedded in the phospholipid bilayer of the cell membrane. These are also called intrinsic proteins.Most integral membrane proteins, called transmembrane proteins span the entire phospholipid bilayer. Transmembrane proteins possess three domains:Cytosolic domain (hydrophilic ; the C-terminus)Transmembrane domain (hydrophobic core of the protein)Extracellular domain (hydrophilic ; N-terminus)

* The attached image illustrates the structure of a transmembrane protein, glyphorin A from RBC plasma membrane.

*Source: V. T. Marchesi, H. Furthmayr, and M. Tomita, 1976, Ann. Rev. Biochem. 45:667; A. H. Ross et al., 1982, J. Biol. Chem. 257:4152.