The above is part of a rendition of the 독립선언서 at 독립문 station.
As someone trying to learn Hanja I find the way that the Hanja is written alongside the Hangul very helpful.
Is there a name for this style of presentation?
There is no specific style of presentation for hangul and hanja being presented side by side. That 독립선언서 was just unique.
If you look at original versions of 독립선언서, they are either written fully in hanja or has a mixture of both (known as the style of 국한문혼용체).
Yes, it's called "국한문혼용체", possibly translated into "Hangul-Hanja Mixed Style". Basically, this style is a transient form widely used while the main character system was being changed from Hanja to Hangul (around the 1900's ~ the 1940's), but this style persists even nowadays in some of the newspapers, mostly because of its space-efficiency. Once this style had been regarded as a more sophisticated style than the Hangul-only style, but today most people do not agree with it. Too bad that I cannot find a good internet material about this topic to introduce you :(.
It is written vertically, so one of the styles applied is “세로쓰기”, which literally means “writing vertically”.
It may be in 국한문체 (國漢文體, Korean-cum-Sino writing style.) also known as 국한문 혼용체 (國漢文混用體), which is a writing style that uses Hanja (Chinese characters) and Hangeul together, usually alternately.
It is written with reading aids; unfortunately, there's no specific word for “writing with reading aids,” as far as I know.
However, a Korean word for referring those reading aids does exist: “첨자 (添字)”, which literally means “an additional letter.” This is similar to Furigana in Japanese.