In "The Daughters of the Late Colonel," what are the nicknames of the two sisters? Why are their nicknames important/significant?

In this short story by Katherine Mansfield, there are two sisters, Constantia and Josephine, whose father has recently died. Josephine refers to her sister Constantia as "Con," while Constantia refers to Josephine as "Jug."
There is no clear distinction made between the characters of the two women in the story. Even after their father, who clearly once laid down the law, has died, they worry about the propriety of such issues as what kind of hat to put on his dead body, fearing he would have protested their choice, and Josephine even fears that they should not have "let them bury father like that." The girls cannot face the prospect of a world without their father in it to tell them what to do, because they never expected to have to look after themselves or make their own decisions.
Constantia and Josephine's nicknames for one another are both monosyllabic, brief, and almost childish. In both cases, the sisters have trimmed down their rather erudite names into the smallest possible diminutive, which echoes the way in which the sisters have both attempted to make themselves as small as possible as presences in life. They never attempted to challenge their father's dominance, and they can barely dare to do so even in his death.
Josephine's nickname, "Jug," might suggest that she is a vessel, an empty pitcher, into which others' thoughts and feelings are poured; a jug is also a utilitarian household item, something to be used. However, when it is not being used, it does not really serve any purpose. Without her father, Josephine is afraid to act, seemingly aware that she is now purposeless.
"Con" recalls the infinitive "to con" and the noun "con," suggesting a sham. From this, we could interpret that Con has been "conned" by her father and the society around her into a fear that she and her sister will be "blamed" for any decision they make. We could also make a connection between the idea of a "con" and the denial Constantia feels about what has really happened. When Josephine and Constantia decide to tackle the question of their father's bureau, Josephine becomes convinced that her father is somehow hidden inside it, and Constantia says, "Don't let's open anything. At any rate, not for a long time." Her only bold act in the story—"one of those amazingly bold things that she'd done about twice before in their lives"—is born out of this denial: she "turned the key" in the wardrobe and shut it out of sight so that neither she nor her sister would have to truly face their new reality.