I originally thought so, too. Surprisingly, both have been using the "Holy War" moniker (though BYU v Utah seems to use it a bit more, since they play much more regularly than Notre Dame and Boston College do on the weird " 5 ACC teams playing Notre Dame" scheduling system, which seems to have the two only play every other year now.)
The Notre Dame/Boston College game has been using the title since 1975, when the media began calling it a “Holy War” game due to both schools Catholic affiliations, and the name stuck. (I was also curious about when BYU-Utah started to call its game the Holy War but was unable to find a year, oddly enough.)