What is the name of LaTeX's default style and why was it chosen for LaTeX?
If you make a LaTeX document without using many packages and without altering other defaults, then the style of the document is largely determined by two factors: the default font designed by Donald Knuth, and the default layout of the standard document classes designed by Leslie Lamport.
The Font
The default font is Computer Modern, designed by Donald Knuth. It is a computer version of the "modern" style typeface that was used in the first editions of his book The Art of Computer Programming. Knuth created TeX with the primary goal of using the computer to typeset this book.
Page Layout, Margins, Headings, etc.
The basic LaTeX document classes were designed by Leslie Lamport, based on then-common conventions for scientific publishing. For example, the large default margins in the article class are intended for use by academic journals, which have a narrow type block, and would trim down the page to fit their format.
These core classes have most of the style elements hard-coded into them, meaning that the style decisions cannot easily be modified by the user. This was because of the memory restrictions of computers at the time. Now we can use packages to alter these values, or we can use alternate classes that make it easier to customize.
Paragraph Shape, Character Spacing, Kerning, etc.
A third factor that shapes the overall look of any LaTeX document is the unsurpassed algorithm for building lines, paragraphs, and pages, used in the core TeX typesetting program written by Donald Knuth. This central feature of the TeX program controls the distribution of words on the page, which creates what designers call the "grayness" of the page. Some people claim to be able to recognize TeX-produced documents based on this alone.
Going Beyond the Defaults
If you use a different font package (try ebgaramond or newpxtext or gillius for example) the look will change dramatically. If you use a non-standard document class (beamer, memoir, the KOMA-script classes) or customize the standard ones by using packages like geometry, or write your own class, you can have any page layout and style you want.
You can also use an alternate format, ConTeXt, which provides its own interface for customizing the layout.
Or you can use Knuth's original Plain TeX format, though this requires you to write almost all the formatting code yourself, down to exactly how much stretchable space to insert after a section heading or in front of a bullet point.
Donald Knuth typeset the later editions of The Art of Computer Programming using his own macro package for Plain TeX, and if you look at that book you'll see his stylistic preferences are rather different from those of the default LaTeX classes, such as using sans-serif font for headings and slanted type for book titles.
In LaTeX there is no unique style -- we've got a collection of macros based on the LaTeX core (which itself uses the primitives of TeX, originally developed by D.E. Knuth in the late 70s/early 80s -- Mr. Knuth also provided the cm fonts)
About 1985 Leslie Lamport developed LaTeX as macro package based on the not very easy usage of Knuth's TeX language (My personal view). He aimed to simplify often used document settings (margins, chapters etc, title pages etc.) in a bunch of (many ;-)) LaTeX commands. He was definitely guided (as well as others (still) contributing to LaTeX) by good typography design which commanded some settings.
Nowadays we use \documentclass as the 'style' for particular purposes and macro packages which add some functionality or change the style too.
There are some settings in latex.ltx (the core of LaTeX) and the base classes do have .clo files (class option files) where the bootstrap settings are stored.
Since some of the standard classes (see below) use the article.cls as bootstrap (via \LoadClass{article}) the settings in article.cls propagate to other classes as well.
However -- we can basically change anything (with some exceptions).
Very often used document classes are
articlebookreportletter
Those are called standard document classes because they are provided with any LaTeX distribution in the base directory.
Other people provided further classes such as
memoir- The
KOMAequivalent of the article, book and report beamerfor making screen presentations (but handouts too)
Publishers, magazines etc. often have a class of their own which fits their needs.