I've heard basically three histories, and I'll attempt to give my lay-person summary of them all:
The Assassin cult used drugs and mysticism to motivate agents before suicidal(or nigh so) tasks, and got known for using hashish to this end. Thus, they were known as 'users of hashish' which eventually became the word for Assassin.
There is no actual connection between hashish and the assassins, the result being bad translation of arabic by westerners presuming the words had anything in common when they in fact did not. The connection is purely some form of western backronym.
The assassin cult was the object of plenty of ridicule (for numerous reasons, political, religious, etc) and were effectively tied to the drug as a form of slander, an attempt to discredit them. Their contemporaries claimed they were drug users or addicts to minimize their influence. This may or may not be a parallel name to another name they had.
Reading the wikipedia article I think all three of these are espoused in different places which just makes me more confused. Is there something I'm missing that makes these make sense together, is one of these predominant? Are they all independently true, in a sense?
I'll try to answer your question, sorry if it doesn't satisfy you (especially since this isn't my area of expertise)
So far, it's kinda the combination of 2 and 3. The first time the Nizari Isma'ilis were called "hashashin" was in 1122, where during a feud between the Nizari and Musta'lian Isma'ili the Fatimid caliph Al-Amir who supported the Musta'lians called the Nizaris 'hashishiyya', without any explanation. However, the name is rarely used by the Muslim authors who prefer to designate the Isma'ilis as 'Isma'iliyya' or 'Nizarriya' if not using derogatory terms like 'malahida'. However, a few contemporary Muslim historians, mainly from the 13th century occasionally use the term 'hashishiyya' in reference to the Nizaris of Syria while the Nizaris of Persia, are also called 'hashishi' in some Caspian Zaydi texts. But in all these Islamic sources, the terms 'hashishi' and 'hashishiyya' are used in reference to the Nizaris without any derivative explanation.
So what exactly is 'hashishiyya'? It's a plural of 'hashish', a term for herbage, more particularly dry herbage or fodder. Later it was specialized to refer to Indian hemp, cannabis sativa aka hashish, but the common word for hashish consumers were 'hashshash'. While some Muslim writers as aforementioned to refer the Nizaris as 'hashishiyya', they never used 'hashshash', let alone accuse the Nizaris of using hashish. So why did they use the term? As point 3 suggests, it's for slander. The Nizaris were viewed with hostility by other Muslims and would easily qualify for every sort of derisive judgement on their beliefs and behaviour. So while the term refers to hashish, the term is used only in its abusive, figurative sense of 'low-class rabble' or 'irreligious social outcasts' because to mock an already despised minority sect even harder is to associate them with the prevailing vices at the time
Of course the European Crusaders, ignorant of general Muslim beliefs and the Isma'ilis around them started to interpret the word wildly. The Nizari isma'ilis and the Crusaders had numerous confrontations in Syria, which had important consequences in terms of the distorted image of the Nizaris in Europe. The first of such encounters dates back to the opening decade of the 12th century. Later, the Nizaris and the Crusaders sporadically fought each other over various strongholds in central Syria. But it was not until the second half of the 12th century that travellers, diplomatic emissaries and chroniclers of the Crusades began to write about the strange sectarians, the followers of a mysterious 'Old Man of the Mountain', or 'le Vieux de la Montagne', who were designated by them in different European languages by variant forms of the term 'Assassins'. At that same time, the Frankish circles and their chroniclers started to fabricate and circulate, both in the Latin East and in Europe, a number of tales about the secret practices of the Nizaris. It is important to note that none of the variants of these tales are found in contemporary Muslim sources, and Nizari texts themselves never mentioned the usage of hashish of any kind. The Crusaders were particularly impressed by the highly exaggerated reports and rumours of the Nizari assassinations and the daring behaviour of their fidais, the devotees who carried out targeted missions in public places and normally lost their own lives in the process. That's why these fictions revolves around the recruitment and training of the fidais, because they were meant to provide explanations for behaviour that would seem irrational or strange to the medieval European mind. These so-called Assassin legends consisted of a number of separate but interconnected tales, including the 'training legend' (strict training and emphasis on obedience from childhood), the 'paradise legend’ (the supposed paradise garden), the ‘hashish legend’ (using hashish to increase solidarity and bravery), and the ‘death-leap legend’ (leaping to their death from high towers in a show of loyalty to the order, probably accompanied by an eagle shriek too). The legends developed in stages and eventually culminating in a synthesis popularized by Marco Polo.
Sources/Bibliography
The Isma'ilis, Their History and Doctrines by Farhad Daftary
The Assassins, Radical Sect in Islam by Bernard Lewis
The Order of The Assassins by Marshall Hodgson
The Encyclopaedia of Islam Vol 3 H-IRAM by Bernard Lewis et al
Follow up question. Is this what assassins creed was based on?