"Eight-layered" is doing exactly the work in Japanese that "eightfold" would do in English — it's not a literal count, it's an intensifier borrowed from the language of court poetry. The compound 八重 shows up all over Heian-era waka (八重桜, 八重霧, 八重垣) as shorthand for "many, thick, overlapping," and Gotouge is drawing on that same shelf of vocabulary rather than inventing a new coinage. VIZ's "EIGHT-LAYERED MIST!" keeps the numeral literal, which is a reasonable call for an attack name shouted mid-fight — but it does lose the poetic register a Japanese reader picks up instantly, the same way an English reader hears something different in "a thousand cranes" than in the literal count.
What makes 八重霞 worth a second look is that it's the one Mist Breathing form the corpus can confirm Muichiro uses twice, in two very different fights three volumes apart — first as a mid-tier technique against an Upper Rank's summoned demons, then again as one beat in the opening exchange against Muzan himself. The corpus's own page-alignment tooling actually misfiles the second occurrence (Vol. 19, p.97): its stored English text drifts onto the wrong JSON page, attaching "EIGHT-LAYERED MIST!!" to a different form's Japanese line entirely. The real VIZ page (Vol. 19, p.98) confirms the name is unchanged from the Vol. 14 appearance — Eight-Layered Mist reads the same whether it's aimed at a demon's slime-fish or at the progenitor of all demons, which says something about how early in Muichiro's repertoire this form sits: it's foundational enough to still be load-bearing in his final fight.
Structurally, Eight-Layered Mist pairs with Scattering Mist Splash (Form Three) as the style's two "volume" techniques — where Form One is a single clean strike, Forms Two and Three both describe mist doing something en masse (many layers; scattering droplets), suggesting Muichiro's early forms build outward from a single cut into wider fields of obscuring mist before the later forms (Five, Six, Seven) start bending time and visibility itself.