What is the name/term for someone's personal writing style?

It is their signature (writing style) - as unique as their (handwritten) signature.

ODO:

signature NOUN

1.2 A distinctive pattern, product, or characteristic by which someone or something can be identified:
‘the chef produced the pâté that was his signature’
[as modifier] ‘his signature dish’

quiddity

A distinctive feature; a peculiarity.
- ‘Imitating the great singers with full respect to their quiddities and idiosyncrasies isn't easy.’

Merriam-Webster says it originally derived from Medieval Latin quidditas, which means essence, composed from the Latin quid; ‘what’, and the neuter quis, the interrogative pronoun for ‘who’. In Italian it is quiddità.

You could mention “the quiddity of a person's writing style/voice”.

idiosyncrasy

1.1 A distinctive or peculiar feature or characteristic of a place or thing.

In a paper entitled Idiosyncratic Expression: Stylistic Analysis the academician claims that the peculiar style and choice of words help identify the author of a written piece of work and allow readers to glimpse into the writer's inner psyche, which is not otherwise exposed.

The writer's individuality is expressed by the writer's language. The term "language" is too broad, but stylisticians have reduced it to mean only vocabulary, syntax and images. More often finding the irregularities in the vocabulary or syntax has become important in the stylistic analysis. J. Middleton Murry calls this irregularity "idiosyncrasy"(5), other critics call it a "deviation from the norm." [...]. In other words, the irregularity reflects those suppressed features of the psyche or personality that surface from the deep which reflects the man behind the words.

From Murray's book, THE PROBLEM OF STYLE (1922)

In the first of these sentences ‘I know who wrote the article in the Saturday Review — Mr. Saintsbury. You couldn't mistake the style’, ‘style’ means that personal idiosyncrasy of expression by which we recognize a writer. Many elements go to make up this individuality. One of the best ways of distinguishing them and discovering the order of their importance is to play that excellent game of guessing the authorship of passages.

Finally, if you can identify someone's style of writing, singing, or painting, it is said to be

unmistakable

not likely to be confused with something else; clearly recognized
Not able to be mistaken for anything else; very distinctive:

• His guitar style is unmistakable.
• ‘His style is undeniable and unmistakable, but one hopes he has few admirers.

Sources: Cambridge, Oxford Living, and Macmillan Dictionaries

Whether you're looking for a term other than this I can't be sure, but most writers I know, including myself, call it prose.

:written or spoken language in its ordinary form, without metrical arrangement [Merriam Webster's]

Tom Clancy's entertaining prose makes him a successful writer even if his story is less than exciting.

The term writeprint is a specific term used in the field of stylometry research. According to Wikipedia:

Writeprint is a term proposed by some forensic linguistics researchers to denote a set of distinguishing stylometric characteristics of a written text (writer invariants) such as "vocabulary richness, length of sentence, use of function words, layout of paragraphs, and key words" which allow one to identify its author (if written by a single person).

The word I believe you are looking for is... DICTION

I went on the same search as you and came up fruitless after numerous searches, then cross-referenced idiolect with a few different search terms and found it!