I'm confused about how I should hyphenate these words because MS Word often suggests something like this: an-yone, an-ymore. According to Google, MS Word is right and we can hyphenate them in two positions: an-y-one, an-y-more. But sites like hyphenation24.com and hyphenator.net disagree with that, and according to them, there's only a possible way we may hyphenate these words: any-one, any-more, any-thing.
The UK and the US tend to differ on how to hyphenate. British printers have tended to follow etymology, American printers will hyphenate at any syllable break.
Strictly following the American rule gives "an-y-one". However a break after the "y" seems to be preferable for most readers. Hyphenation is a bit of an art. Implementing that art as a computer algorithm is tricky. Sometimes computers get it wrong.
For what it is worth TeX hyphenates as "any-one", even with American hyphenation patterns.