How common/normal would nicknames, that kind of stem from a not-so-super amazing deed (but deed nonetheless) but weren’t given by a scop and are therefore not ‘the one name’ be?

I don’t know if the presence of scop names effects it in Wintermark, but nicknames are present in the other nations to about the extent they are in the real world - perhaps slightly more, because there are lots of people who have names that sound complicated or difficult to people from other nations, who they meet with once a season, so a nickname is often helpful.

A nick name for regular things would be entirely fine. A Hero’s Name (as told by a Scop for a heroic tale) is different and would be respected as such.