In the 'History of Alamut' there are at least four etymologies given for the word assassin.
User of hashish
Follower of Hassan
Below I've included excerpts from various sources which argue the 'correct' etymology of the term. Generally contemporary Isma'ili sources reject the 'hash' root entirely (though do not, interestingly enough, reject the Alamutis 'terrorist' reputation) as demeaning to Isma'ilis.
Myth : The word assassin is derived from the word hashish.
It is a common myth that the word assassin comes from the Arabic word haschishin for hashish user.
The story is that al-Hassan ibn-al-Sabbah used hashish to enlist the aid of young men into his private army known as assassins (aschishin - or follower of Hassan). One of the primary sources for this information comes from the writings of Marco Polo who visited the area in 1273, almost 150 years after the reign of Al-Hassan.
There are many conflicting facts and sources for this information.