It occurred to me that there is no question on here about the name "normal distribution" yet.
There is this question, about whether to call it normal or Gaussian, but it does not address why it is called normal in the first place.
The normal distribution is not a typical/ordinary/expected result of many processes, so why is it called normal?
Summarising info from the links from Glen_b and Gordon Smyth in the comments:
From wikipedia, which credits (blames?) Gauss.
Gauss himself apparently coined the term with reference to the "normal equations" involved in its applications, with normal having its technical meaning of orthogonal rather than "usual".[76] However, by the end of the 19th century some authors[note 5] had started using the name normal distribution, where the word "normal" was used as an adjective – the term now being seen as a reflection of the fact that this distribution was seen as typical, common – and thus "normal". Peirce (one of those authors) once defined "normal" thus: "...the 'normal' is not the average (or any other kind of mean) of what actually occurs, but of what would, in the long run, occur under certain circumstances."[77] Around the turn of the 20th century Pearson popularized the term normal as a designation for this distribution.[78]
Many years ago I called the Laplace–Gaussian curve the normal curve, which name, while it avoids an international question of priority, has the disadvantage of leading people to believe that all other distributions of frequency are in one sense or another 'abnormal'.
— Pearson (1920)
The main source cited is Jaynes, Edwin T.; Probability Theory: The Logic of Science, Ch. 7
Some contrary claims crediting Galton and (to a lesser extent) Peirce:
According to Kruskal & Stigler, the term normal was used, apparently independently, by Charles S. Peirce (1873) in an appendix to a report of the US Coast Survey (reprinted in Stigler (1980, vol. 2), Wilhelm Lexis Theorie der Massenerscheinungen in der menschlichen Gesellschaft (1877) and Francis Galton 'Typical laws of heredity' (1877).
Of the three, Galton had most influence on the development of Statistics in Britain and, through his ‘descendants’ Karl Pearson and R. A. Fisher, on Statistics worldwide. In the 1877 article Galton used the phrase "deviated normally" only once (p. 513)--his name for the distribution was "the law of deviation." However in the 1880s he began using the term "normal" systematically: chapter 5 of his Natural Inheritance (1889) is entitled "Normal Variability" and Galton refers to the "normal curve of distributions" or simply the "normal curve." Galton does not explain why he uses the term "normal" but the sense of conforming to a norm ( = "A standard, model, pattern, type." (OED)) seems implied.
Karl Pearson wrote, in his "Contributions to the Mathematical Theory of Evolution," Philosophical Transactions of the Royal Society of London. A, 185, (1894) p. 72, "A frequency-curve, which for practical purposes, can be represented by the error curve, will for the remainder of this paper be termed a normal curve." Later Pearson seemed to imply that he had introduced the term: "Many years ago I called the Laplace-Gaussian curve the normal curve ..." (Biometrika, 13, (1920), p. 25). While Pearson did not introduce the term, it is fair to say that his "consistent and exclusive use of this term in his epoch-making publications led to its adoption throughout the statistical community." (DSB) Curiously a main theme in Pearson’s scientific work was that data did not ‘normally’ follow this distribution and that alternative distributions had to be devised. (See the entry on Pearson curves.)
Once the basic normal terminology was adopted NORMAL appeared in many expressions. These must have seemed more or less obvious to their creators and were probably re-invented many times.
