The Monster group was investigated in the 1970s by mathematicians Fricke, Andrew Ogg and John G. Thompson; they studied the quotient of the hyperbolic plane by subgroups of SL2(R), particularly, the normalizer ?0(p)+ of ?0(p) in SL(2,R). They found that the Riemann surface resulting from taking the quotient of the hyperbolic plane by ?0(p)+ has genus zero iff p is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59 or 71 (that is, a supersingular prime), and when Ogg heard about the Monster group later on and noticed that these were precisely the prime factors of the size of M, he wrote up a paper offering a bottle of Jack Daniel's whiskey to anyone who could explain this fact.
... I am not going to explain what this means considering with words like supersingular prime, I only barely vaguely understand what it states (algebraic topology, it looks - studying quotient groups of hyperbolic plane - an example of a structure formed by taking a quotient of a more general structure, say a plane is a torus) but there is a simple point in this.
This explanation for the origin of the name seems like reaching, it is akin to a backronymn as an example of something explained after the fact to match the event. A more likely viable explanation is that offered prior:
The term "monstrous moonshine" was coined by Conway, who, when told by John McKay in the late 1970s that the coefficient of q (namely 196884) was precisely the dimension of the Griess algebra (and thus exactly one more than the degree of the smallest faithful complex representation of the Monster group), replied that this was "moonshine" (a word that is used in English as a moniker for crazy or foolish ideas). Thus, the term not only refers to the Monster group M; it also refers to the perceived craziness of the intricate relationship between M and the theory of modular functions.
The point of this post is two-fold. To show how psychological notions affect how we name things and then how subsequent generations interpretate things based on schemas in use when introduced. This in turn shapes the evolution and form an entire subject takes. For example, Conway percieved a coincidence and craziness in what logically follows from a set of premises. The idea of craziness, naturulness, obviousness have no place in the mathematical world. These things are significances which are entirely imaginary, reflecting biases and due to a lack of full understanding (due to the newness only not any lack of skill, Conway is a flipping genius). Unfortunately the stigma introduced into a foreign new concept often colour it in a way which make it unclear, this is then carried to subsequent generations. Adding baggages of understanding which need not exist.
Secondly, by carefuly choosing a name much confusion may be elimanated in the introduction of a subject. Just because it looks like a duck does not mean it is a duck. It may be a sheep in duck's clothing. The name monstrous moonshine group is sufficiently ambigious to be a good mathematical name. By naming it as such, people do not enter into the subject with preconceived notions due to name sharing and thus they do not wrongly or inappropriately transfer old concepts into this new schema which in the future cause dissonance and conflicts, resulting in confusion and disunderstanding. An empty cup is easier to fill with clear water than one partway filled with mud.
It is important to name new concepts carefully and in a way which discourages pre-assumptions.