Hill's system alphabetizes elements symbol or name? Take monosodium glutamate.
Its chemical formula is $$\ce{C5H8NO4Na or   C5H8NNaO4}$$
First way nitrogen, oxygen, sodium, with is in order of element's name.
Second way, N, Na, O, in order of element's symbol.
Have seen it both ways, hoping someone could clarify. Thanks.
Go straight to the original source, ON A SYSTEM OF INDEXING CHEMICAL LITERATURE; ADOPTED BY THE CLASSIFICATION DIVISION OF THE U. S. PATENT OFFICE, and you can see that Hill uses the element symbol to determine alphabetical order.

In your example $\ce{C5H8NNaO4}$ is correct.