Navi, Aria, and Lilly are the Silverblade family fairies, though they are techincally Kokiri fairies and the reasons the Silverblade family was given them to keep are, needless to say, flimsy. Despite the fact that they were each appointed to an individual member of the family, they are often seen and discribed as a triumvirate and their individual dialogue is very interchangable between the three of them, given their lack of defined personalities.
As any one who is familiar with The Ocarina of Time canon would know, Navi is Link's fairy. The difference of her role in My Inner Life to that of OOT canon is that she was not in Link's company only for as long as he needed to defeat Ganon, but that she became his fairy companion forever (which, as mentioned, makes no sense given he is not actually a Kokiri). Though it is never explicitly stated, she gives off the vibe of being the leader/most dominant out of the three, given she is the one who usually speaks for them...or this may just be her talkative nature, as seen in OOT, coming out in the fanfic and a rare display of the author actually maintaining canon traits.
Lilly is Jenna's (unfairly) appointed fairy. She really has no personality whatsoever, or at least none that can be especially distinguished from her other two companions. She may be a little dimwitted, however, as it seems to take her awhile to catch on to things.
Aria is Link Jr's appointed (obligatory) fairy. She has so very little of a personality or character presence that even the author will sometimes forget to mention her.
The Silverblade's are given Navi, Lilly and Aria with the logic that they will protect them should "Gannon" return. This fails to take into consideration the fact that fairies cannot do much (or anything, really) in the way of protection and that there was never any indication that "Gannon"'s return was at all emminent. Saria perhaps gave insight into the real intention behind this when she explained to Mido that Link is "special and so is his wife.", meaning that Link and Jenna were given the fairies by the author just because.