Word for the direction of written words

English moves left to right. Hebrew moves right to left. Both then move top to bottom. Mongolian moves top to bottom, and some Philippine languages move from bottom to top.

Is there a word that names the idea of these conventions?

The question was really answered by michael.hor257k in the comments, but I think someone should write an actual answer, too.

The name for the concept is script directionality. For examples of usage of that term in academic literature, see e.g. here, here, here...

Omniglot has an index of languages according to writing directionality, here.

Some examples and associated names for particular script directionalities:

Horizontal scripts

The overwhelming majority are read starting from the top row and moving down, i.e. top to bottom.

Left-to-right, also known as rightward (see e.g. here) and dextroverse (see e.g. here). Examples: the Latin script (as used in e.g. English), the scripts of the languages of India, and much of modern Chinese (source). For many more examples, see here.

Right-to-left, also known as leftward (see e.g. here) and sinistroverse (see e.g. here). Examples: modern Arabic and Hebrew, and ancient Etruscan, Cypriot, Aramaic, and Phoenician. For more, see here.

Boustrophedon (from Ancient Greek bous ox, cow + strephein to turn) also known as plough-wise (see e.g. here). In this script, 'every other line of writing is flipped or reversed, with reversed letters' (source), like this:

House
ǝƨuoH

(This effect can be produced here.)

In other words, every other line employs mirror writing, which is the mirror image of normal writing: it appears normal when it is reflected in a mirror, like on the front of ambulances, where the word "AMBULANCE" is often written in very large mirrored text ("ƎƆИA⅃UᙠMA"). Examples: some early Greek writing (here), and some other ancient scripts, including Hungarian Runes, Linear B, Rongo Rongo, Sabaean (source).

There is also false boustrophedon, where the writer simply turns the writing surface by 180° and continues writing in the same direction as in the previous line, for example like this:

house
ǝsnoɥ

(That can be done here.)

Example: also some ancient Greek writing (see e.g. here).

In all the examples above, the text is read beginning with the top row and going down. The only known exceptions to this pattern are the scripts of Philippine languages of Tagbanwa and Hanunó'o, and the Batak language of Sumatra, which are read left to right starting from the bottom row and moving up. Interestingly, since they are written on vertical strips of bamboo held together with string, they are written in vertical columns along the strips, and then read horizontally across the strips. All three 'are closely related, all being descended from the Kawi script, which came from the Pallava script, which ultimately derived from the ancient Brahmic script of India. These scripts are syllabaries (like the Devanagari script of India).' (source)

Vertical scripts

Most commonly, columns are read top to bottom.

Example of scripts where one starts with the leftmost column and moves to the right: Old Elamite, Manchu, Mongolian, Oirat Clear Script, Phags-pa, Sogdian, Sutton SignWriting, and Uyghur (source).

Examples were one starts from the rightmost column and moves left: modern Japanese tategaki, traditional Chinese and Korean, and several other scripts, both modern and ancient (source). Note that Japanese, Chinese, and Korean can in principle be written in either vertical or horizontal fashion; see below.

Again, as a rule, the text runs top to bottom. The only known exception is the ancient Berber script, where 'most inscriptions are written in vertical columns running from bottom to top starting either on the left or the right. Monumental inscriptions generally run in horizontal lines from right to left' (source). The above-mentioned scripts of Tagbanwa, Hanunó'o, and Batak are written bottom to top in vertical columns (along vertical bamboo strips), but they are usually read left to right.

There do not seem to exist any scripts which are 'vertically boustrophedon', which would presumably look like this (right-to-left version):

e  H
s  o
u  u
o  s
H  e

(I think that there is no need for the individual letters to be vertically flipped, so that this is the true vertical boustrophedon; and I think the reason has to do with this old chestnut. But I could be wrong.)

Scripts with variable directionality

Ancient Egyptian (Hieroglyphic)

The Ancient Egytian Hieroglyphic script was written in any direction the was convenient: horizontally from right to left or left to right or vertically from top to bottom. The arrangement of the glyphs was partly determined by aesthetic considerations. When written horizontally, you can tell the direction of a piece of writing by looking at the way the animals and people are facing: they look towards the beginning of the line.

Etruscan

Etruscan was sometimes written in boustrophedon fashion and sometimes from right to left in horizontal lines.

Ogham

When inscribed on stones, Ogham was written around the edge starting at the bottom left and running upwards then back down the other side. In manuscripts it was written horizontally running from left to right.

And among modern languages,

Chinese

Chinese can be written from right to left in vertical columns, left to right in horizontal lines, or occasionally right to left in horizontal lines. In Taiwan it is often written vertically, while in China and Singapore it is usually written horizontally. In newspapers and magazines with vertical text, some of the headlines and titles are written horizontally right to left across the top of the main text.

Japanese

Japanese can be written from right to left in vertical columns or left to right in horizontal lines. Horizontal writing was first used during the Meiji Period (1868-1912) in Western language dictionaries of Japanese. Today both orientations are used.

Korean

Until the 1980s Korean was usually written from right to left in vertical columns. Since then writing from left to right in horizontal lines has become popular, and today the majority of texts are written horizontally.

(source)