Essentially, 'Chrono Trigger' is no thing, and no person. It is an idea and concept. It is a descriptive noun, with trigger being the main noun, and Chrono being the adjective describing which sort of trigger it is. Chrono is, let me check the lexicon to be double sure... XPONOS (forgive me for the last symbol; it should be a sigma, but it appears the ASCII symbols aren't giving me most of the Greek.) Anyway, it's Greek which, according to the lexicon I have, is the word for time. But I think we all knew that it meant time, already.
Now, that aside, the point that must be stressed is that this term can be technically applied as a descriptive noun to anything that causes a sudden change in time, by nature of the meaning of the name. Crono is a Chrono Trigger, as is Serge, as is the pendant, etc. However, in the context of the game, only certain elements of paramount importance are given the title. The first is the well known Time Egg (or, rather, first Time Egg; there are at least two and a half of these things floating about the various worlds.) It triggers an effect in time (in the case of the first one, an absolute halt that even the most powerful of people thought impossible, and in the case of the second a means by which to traverse dimensions.) Thus the effects are many and varied and, in my opinion, are dictated by the whim of fate and need, rather than any set function. Thus, generally speaking, these are 'true' 'Chrono Triggers.'
The second time the term is used is questionable. It is only once said to be Serge (and, in my opinion, is thrown in by the writers to give it an early connection to the first game, not out of any actual reason.) However, he, too, may indeed be seen as a thing that effects time enough to warrant such a title. It is his death that is used as the catalyst, the trigger, to split the worlds, allowing the forging of the Chrono Cross. He was the neccessary piece in causing such a unique effect in dividing dimensions and, looked at as a thing of function rather than a person, may be seen as triggering the desired effect in time.
Now, why aren't other things named this? Why is not the pendant, or the telepod, as they have a profound impact upon the flow of time, not named as such? Perhaps they can be, but the writers did not think so deeply on the matter. Another explanation might be that neither effects time directly, or not in a great manner. They serve as transportation, moving those who actually change time along in their journeys. Aside from the causing of something to exist in a time when it should not be, they do not actually change the flow of time, any more than a connection between two roads affects the traffic upon either: it is the cars that merge from one into the other that truly change this. It might be debateable that the earliest affector might be seen as the true 'trigger', and thus the telepod and the like, but more than this I cannot figure through. Using this rationale Serge would also be a Chrono Trigger... but so would all Seven in the first game.
Yet, perhaps the description needs to be more specific: that which actually changes the flow itself. Crono and the company are like those that throw sticks into a river, thus changing its end result. Time still goes from point A to B or, in the worst of scenarios, from A to C in a single line. The Time Eggs, however, actually stop the flow, changing the inherent nature of the 'river'. No longer is it a moving entity going from one point to another. It has ceased moving. The same is true for Serge. He splits it into two, changing the basic premise of a single continuing line. Thus a 'Chrono Trigger' might be seen as that which changes the established defenition of time. This, I might add, is exactly what the last person said in their post... I have merely elaborated on the subject and put it into less concise words, so to speak, and tied it together with the Time Eggs.