Also, is it something that was added by historians after the fact, or were they generally given during a monarch's reign? (Presumably some, like Charles the Bald, wouldn't have liked this).
For both Louis the Pious and his son Charles the Bald, these were both names by which they were known during their lifetimes. As for Charles' opinions on his nickname, we've no record of how he felt about it, but he might well have like it and found it funny, since it's possible that it was ironic, and that he was in fact an unusually hairy man - given that we know the name was used during his lifetime and any contemporary depiction of him has a full head of hair.
As for the why, I'm not sure I can answer that one. It does help to distinguish between kings with the same name who ruled around the same time (like all the later Louis' in French history), but given that Louis the Pious was also Louis I, that doesn't really hold up. I've never read an explanation of it, to be honest - sorry!