Etymology of "normality"
The term &quot;normality&quot; stems from the older German term for equivalent concentration (die Äquivalentkonzentration), namely die Normalität, which was coined by Karl Friedrich Mohr.
According to German Wikipedia which also refers to Straube's Der historische Weg der Chemie [1, p. 220], Mohr introduced the concept of normal solution and normality (as it's known in the modern world) in the first edition of his Lehrbuch der chemisch-analytischen Titrirmethode [2], e.g. the preface contained the following definitions among others:

Die Normaltemperatur der Flüssigkeiten ist 14° R. = 17,5° Cent.
[…]
Normalflüssigkeit bedeutet eine Lösung, welche 1 Atom Substanz, in Grammen ausgedrückt, in 1 Litre enthält.
Zehend-Normalflüssigkeit bedeutet eine Lösung, welche $1/10$ Atom Substanz, in Grammen ausgedrückt, auf 1 Litre enthält oder mit $1/10$ Atom eines darin enthaltenen Körpers (z. B. Sauerstoff) wirkt.

The book also lists numerous &quot;normal&quot; definitions not really in a sense of &quot;adequacy&quot;, but rather in a a sense of &quot;standard&quot;: Mohr basically invented standardized quantitative analysis and proposed numerous analytical tools and techniques.
Among these definitions there are:

Normalwägung — standard weighing [procedure];
Normalbürette — standard burette (a glass tube $\pu{500 mm}$ long, $\pu{13.5 mm}$ inner diameter, holds $\pu{60 cm3}$ of liquid divided into five parts, each $\pu{cm^3}$ is $\pu{7 mm}$ long);
Normale Stärke — strength of a normal solution of acid/base;
Normalsäure and Normalnatron — standard/normal solutions of acid and soda, which, interestingly enough, Mohr suggested to label with the pieces of red and blue paper, respectively;
Normalkleesäure, Normalsalpetersäure, Normalchlorbaryum, etc. — normal solutions of oxalic, nitric acids and barium(II) chloride and so on.

At the same time, normality was used to describe the normal ratio between stoichiometry of the elements (esp. C, O, N) and the number of found equivalents in complex compounds such as proteins or drugs [3].
References

Wilhelm Strube: Der historische Weg der Chemie. Aulis Verlag Deubner &amp; Co KG, Köln 1989, ISBN 3-7614-1180-4. (In German)
Friedrich Mohr. Lehrbuch der chemisch-analytischen Titrirmethode; Vieweg und Sohn: Braunschweig, 1855. (In German. Available for free at Google Play (accessed 2019-05-25))
Zeising, A. Das Normalverhältnis der chemischen und morphologischen Proportionen; Weigel, 1856. (In German. Available for free at Archive.org (accessed 2019-05-25))