"Triskele" is unrelated to "Triste"
It is more likely that "Triskele" is used in the sense of a design in the form of three running legs (or stylizings thereof) arranged at 120-degree angles with the "hip" being the center of a circle. Merriam-Webster online gives the term as a variant of "Triskelion". Triskele has three legs (and a stump, but perhaps
Such a design serves as the symbol of the Isle of Man see <http://www.crwflags.com/fotw/flags/im.html>. It would not be un-Wolfean for "Isle of Man" to have some bearing on the choice of the name for the dog. (Hmmm--isolation of Man???) BUT (!!!) the web page mentioned says, "According to Norse mythology, the triskelion was a symbol of the movement of the sun through the heavens".
I was all set to crow at this find just now, but I calmed down enough to check Lexicon Urthus, in which mantis cites John Clute giving an Apollonian connection for the symbol. Darn.
So Severian's healing of Triskele symbolically brings the New Sun, or the New Sun symbolically arises at his touch, or (if we admit what we learn in Urth of the New Sun) the New Sun gives a symbolic token of his coming to the young Severian, which token also sort-of leads him to the Atrium of Time, and also makes the structure sort of cyclic (just like the sun, and like Divine Years), and...
Someone else please pick this up and run with it--my head hurts, and I have to save it for Return to the Whorl :-).
It would also be non-un-Wolfean for the dog character to have been
derived from the symbolic connection.
-- Dan Rabin
P.S. The "-skele" element also occurs in "isosceles".