Every complex matrix can be written as the sum of a Hermitian and a skew-Hermitian matrix. What is this called?
I'm not saying there isn't a name, but it's certainly not universal.
I've been using this decomposition on an almost daily basis for decades, and I don't have a name for it. People usually just say that $A$ is the real part of $T$, and $B$ the imaginary part. Even in the case $n=1$ (i.e., the complex numbers).