It is an honest and requisite move to represent one's university in the least ambiguous way possible. Thank you for doing so.

Some recruiters will not care about the BYU and BYU-I difference. Hiring managers will care though. Whenever I review or interview candidates that claim they went to BYU, I always probe to see if they actually did. (I live in Idaho and have been lied to on the matter before).

As I have stated many times, a math degree from BYU-Idaho will not currently take you as far as a math degree from BYU. I have been overall somewhat unimpressed by many of their math students/department at BYU-Idaho. Sloppy, error filled work, that I have to later go back and fix. There is a distinct difference in my opinion. If that makes me elitist, so be it.