I didn't wanna ask because it's probably really obvious, but

What are the icons next to your level and class mod name on the HUD? As nisha I have a little icon with a stack of coins, but it’s not always the same - sometimes it’s a bottle, sometimes it’s a skull?

i think that has to do with the your badass rank. it changes icon after certain number gained.

Maybe it’s somethingr to do with your last challenge completed?

maybe

It changes depending on how high your Badass rank is.

Correct, it only has to do with what your Badass rank is

I tried tracking it here, but wound up going back to BL2, and haven’t been back.