You're in the realm of typography and word processing here, really, aren't you? About 'how the words show up on the page'.
I would call hyphenation, a function of 'word-wrap' - how the words wrap at the right hand margin when justifying text.
Here's a link to a typography page about this, which is really 'a problem' caused by the software incorrectly hyphenating words, which the typographer would aim to catch, and fix, before publication.
You could call it an 'automated word-break', automated hyphen. Or a 'manual word-break', manual hyphen. 'Word-break' - the tendency for words to need to break, is a term you could use.
It's a 'soft-hyphen' if the system software makes it happen automatically - it could be a 'hard-hyphen' if you type in the hyphen manually, or type in another code or codes that manually makes the hyphen occur.
So, 'soft and hard hyphenation', would be term you could potentially use.
You could call it 'justification' - that is the word for everything to do with making the left, right, or both, margins line up and be straight. Which is why hyphenation is necessary, as I'll explain in a moment.
The left margin is 'left justification'. The right, is 'right justification' or 'right justified'. Both, is known as 'full justification' or 'fully justified'.
Both full, and right, justification involves hyphenation - either soft, or hard (automatic, or manual) - because on the right, is where the words have to break, to make a straight line. Obviously left justification only, involves no hyphenation or less hyphenation - as words come to their natural conclusion at the right, unjustified, margin. Only super-long words might have to break, to fit on a line.
The need for hyphenation in justified text occurs where the text, when spread out to fully fill the line space - is insufficient to stretch to fill the whole width. Because a long word flipped to the next line - leaves the preceding line looking - well a bit bare! The justifier then spreads that small amount of text to fill the line...
...That's where you get gaps between letters that c o u l d l o o k s o m e t h i n g l i k e t h i s - which looks ugly and is hard to read, so that is why a word-split is introduced, to allow enough text to be present on a line, to properly fill it, so that the spacing still looks attractive, and the text is pleasant and easy to read.
There's another expression you could possibly use - 'word-split'. I think I just coined that, but maybe it would work!