The Surselva in Graubünden has two big sub-districts (de: Kreise, rm: circuls) in the Rhine valley itself: Disentis and Ilanz.
The German names of those sub-districts are fairly self-explanatory; they are the names of each district's capital town.
In Romansh, however, the names are rather different: "Kreis Disentis" is called "Circul da la Cadi" and "Kreis Ilanz" is called "Circul da la Foppa".
Since the Foppa region is occasionally referred to in German as "Gruob" (presumably corresponding to High German "Grube"), I figured that would be a regular word, and indeed, my dictionary translates "foppa" as "Mulde, Delle, Senke" ("basin, dell, hollow, dent, depression, dip").
But the meaning of "Cadi" was elusive to me. The fact that the kinds of contexts where Kreis Ilanz is referred to as "Gruob" in German refer to Kreis Disentis as "Cadi" in German, too, didn't help, either.
But then I read about the Three Leagues (which later themselves joined together to form Graubünden), one of which, the League of God's Hause (Gotteshausbund) has its own article in the English Wikipedia—and there I read that the Italian name is "Lega Caddea" and the Romansh is "Lia da la Chadé".
And then something clicked. (It also helped that the article used the Rumantsch Grischun version of the league's name rather than the Sursilvan one, since I'm more familiar with RG morphemes).
So, presuming that S "Cadi" = RG "Chadé", I presume that they're both short for "God's house" ("chasa da Dieu" in RG, and word-initial cha- in RG regularly corresponds to ca- in Sursilvan).