There is no single word for a person’s favored punctuation marks.
You’ll have to use a adjective to qualify “punctuation” or a synonym of that noun, or vice-versa use punctuation or some synonym as an attributive noun to modify some other word, as in @Centaurus' fine answer punctuation style.
Which qualifier you choose will depend on the particular flavor you’d like to lend to the description.
Absence of Evidence¹
I say this on the strength of the lack of evidence that the word exists or that there is sufficient need or motivation for such a specific word to be coined.
In support of this conclusion, I'll first point out that the general discipline of identifying authorship from patterns, cues and clues in a text is known as stylometry. If anyone has sufficient reason to coin such a term, it is the scholars of that discipline.
Given that lead, I googled
stylometry glossary and a series of variations on that, both including and excluding punctuation as a term, and found nothing of interest.
The top hit persisted in being the Wikipedia article on the topic. I read that article and found the related term forensic linguistics, and repeated my google searches with that term substituted for stylometry.
Still no glossaries, but I did come across this relatively comprehensive
master's thesis with a full literature review:
INVESTIGATING THE USE OF FORENSIC STYLING AND THE USE OF STYLOMETRIC TECHNIQUES IN THE ANALYSIS OF AUTHORSHIP ON A PUBLICLY ACCESSIBLE SOCIAL NETWORKING SITE
It was authored by Colin Simon Michell in July 2017. Per its TOC, the section that deals with punctuation specifically is 126.96.36.199, starting on page 52. Despite the comprehensive nature of the study and the full literature review of the technical discipline that is most specifically pertinent to your search, that section offers no single-word term for “preferred or idiosyncratic punctuation”.
Consolation Prizes & Work-arounds
However, the thesis does offer us a couple of consolation prizes, multiple-word and/or insufficiently precise though they may be: style markers (not just about punctuation; general "clues") and punctuation devices (not a single word). My instinct is this is the best we will get.
The bottom line is you’ll have to use an adjective to modify “punctuation” or a synonym of that noun. Which adjective you choose will depend on the particular flavor you’d like to lend to the description. You might say “his particular use of ellipses” or “his idiosyncratic punctuation”, etc.
¹ But not, epistemologically speaking, evidence of absence.