Please, note that Newton did not used the "differential" notation, due to Leibniz, but the "fluxional" one : $\dot x$, etc.
See for example :
The moment of a fluent such as $x$ is the amount by which it changes in an indefinitely
small length of time $o$, given by $\dot xo$ , and all products in an equation that involve orders of $o$ greater than one can be ignored.
We can see :
We can find the use of $h$ in :
My "humble opinion" is that there is no special reason for it ...
As long as the symbolism underwent the process of standardization, we can see that the (insufficient number of elements of the) alphabet partecipate to a process of "specialization" :
$x,y,z$ for the unknown; $a,b,c$ for the known terms, mainly in algebra; $i,j,k$ for numerical indices; $n,m$ for naturals;
in addition, $d$ was used for derivative, $f$ was chosen for the "typical" function; $e$ and $i$ acquired a status of proper nouns.
So, there were not many letters available ...