In the series "Divergent" (i.e. Divergent, Insurgent, Allegiant), the only faction of which its members have a nickname is Abnegation, of which they go by the nickname "Stiff".
Why is it that none of the other factions have nicknames at all? I couldn't really find any resources about this here (because there aren't many Divergent questions in here at all), and there isn't anything about it in the books.
Out of Universe - the author's choices dictated a focus on narrative rather than world-building
A focus upon Tris' narrative, and writing the story from her viewpoint (that of someone who spent her early-life in Abnegation), means the story naturally leans towards descriptions of how Abnegation is seen by the other factions. And the decision to make Abnegation a faction that is openly mocked may have been made to engender sympathy from readers towards Tris.
(Credit to "@recognizer" for this point raised in the comments to the question.)
In Universe - Abnegation's unique qualities and responsibilities make them a target (perhaps a greater target than any other faction is) for ridicule, including an unflattering nickname like "Stiffs"
Abnegation is responsible almost solely for the political administration of the city (the exception being Jeanine Matthews). Their position of power and authority leads to resentment among various other factions and faction members, in particular Erudite and their leader Jeanine Matthews. This resentment could be a driver towards the creation of an unflattering nickname for the Abnegation.
Further, the personality of Abnegation encourages selflessness in its members. This trait means that the Abnegation are not predisposed to concern themselves with the names that other factions may give to them. Therefore the Abnegation are not going to defend themselves against ridicule, and as such unflattering nicknames about their faction may pass unchecked between the other factions.
In short, Abnegation is an easy target for ridicule; there is motive to ridicule them, and due to Abnegation's lack of interest defending itself, the ridicule can spread.
We cannot say for certain that other factions are not subjected to any kind of ridicule (they almost certainly are), but it does appear that Abnegation bore the brunt. The reason for this could be that the grudge that Erudite bears towards Abnegation makes theirs the most strained, bitter and divisive relationship that any two factions have in the books. Other factions are likely less-inclined to come up with unflattering nicknames for each other.
Furthermore, at the start of the books Erudite is on good terms with both Amity and Dauntless, and neutral terms with Candor. In many ways they are the most well-connected and (outside of Abnegation's political stranglehold) influential faction in the city. Other factions may therefore have become predisposed to perpetuate ridicule towards Abnegation through their relations with Erudite. (Although doubtless the other factions do not feel as bitterly towards Abnegation as Erudite do, they may have picked up the habit of ridiculing Abnegation by association).
Stiff is merely a nickname, its rather a tease instead. As you know, Erudite feel the need to be rude towards Abnegation. The nickname Stiff is commonly used as Abnegation wear plain, grey clothes to be humble and subtle - grey is also their faction colour displayed by the grey stones used to represent Abnegation at the choosing ceremony.
People who call Abnegation Stiffs are referring to the way the members of Abnegation don't indulge. An example of this would be the fact Tris hadn't had a hamburger before because that would be self-indulgent.
Erudite's hate is displayed in some rather vicious reports released by Erudite against one of Abnegation's Leaders- Marcus, the Father of Four. These reports implicate that Marcus' abusive behaviour towards Four, was the reason for Four to change from Abnegation to Dauntless. The reason that Erudite does this is to suggest Erudite being better as the Government over Abnegation.
Also, in some respects fighting back when people insult you could be considered self-indulgent so that makes Abnegation a easy target.
