Sixteen of the eighteen Armanen runes correspond to characters of the Younger Futhark. Eh is one of the two that do not, and it is where the constructed nature of the row is easiest to see.
Where the name comes from
The name echoes the Elder Futhark character conventionally read as ehwaz, the horse. The Elder Futhark is the older and longer row of twenty-four characters used in the earliest Germanic inscriptions, and it went out of use in Scandinavia well before the Viking age, when the sixteen-character Younger Futhark replaced it.
Why the addition was needed
Guido von List wanted eighteen characters, because the Havamal in the Poetic Edda lists eighteen rune-charms. The Younger Futhark supplied sixteen. Two more had to come from somewhere, and this is one of them, its name taken from the older row that his sixteen did not come from.
That is the whole argument against reading the Armanen row as a transmitted alphabet in a sentence: it mixes two rows separated by centuries in order to hit a number taken from a poem that is not about an alphabet at all.
The frame and the reception
Von List published the row in 1908 and presented it as recovered rather than composed. Runologists do not accept that. The row was afterwards taken up in volkisch circles and by National Socialist organisations in the 1930s and 1940s, and this atlas records that reception plainly.