In a voltage-gated sodium channel, there are two gates, one for activation and one for inactivation. They are also known as h- and m- gate. What are these letters standing for?
Those initials were proposed by Hodgkin and Huxley in their original paper modeling the action potential in nerve cells: https://en.wikipedia.org/wiki/Hodgkin%E2%80%93Huxley_model
They are not names for subunits, domains or motifs in the sodium channel, as your question may imply. Instead,
n, m, and h are dimensionless quantities between 0 and 1 that are associated with potassium channel activation, sodium channel activation, and sodium channel inactivation, respectively.
However, there is no indication of what those initials mean (if anything), apparently being just letters they chose to name the variables in their equations.