I play in a game where - after 10 game sessions, and approximately 4 character levels - the DM has introduced an Honour score for some characters (notably dwarves, and hobgoblins, so far) after watching the Zee Bashew video on it. I play a Dwarf Battle Master Fighter with a history of shame and exile, so I suggested that my Honour statistic be 12 (+1) to show that he has some honour and seeks to redeem his ways, but that he might not the the most honourable character around.
In our game since it's been added as an Ability Score, it's been used a handful of times as an Ability Score Contest, most notably between my character and a Hobgoblin NPC that I tried to "force" to duel my character. Ordinarily, our DM would likely adjudicate this as a Charisma (Intimidate or Persuasion) check. Even though my Charisma(Intimidate) gives me a substantially better bonus than the +1 from my Honour score, I went with the latter since it seemed more in keeping with the narrative: the Dwarf was trying to shame the Hobgoblin into fighting him as a matter of Honour, not cow him in the usual sense.
In an established campaign, it's likely that a character will have acted "honourably" or "dishonourably" at some point. I submit that working with your players to come up with a score that reflects their characters as they've played them, or as they envision them, might be a better way to go, rather than rolling them or generating them some other way. To reflect changes in a character's honour (perhaps especially valid if you'd prefer to start with either a point-bought or rolled score and have a character "earn" their Honour ability score), the DMG p.265 suggests this way for a DM to increase or decrease a character's Honour score during play:
Unlike other abilities, Honor can’t be raised with normal ability score increases. Instead, you can award increases to Honor—or impose reductions—based on a character’s actions. At the end of an adventure, if you think a character’s actions in the adventure reflected well or poorly on his or her understanding of the code, you can increase or decrease the character’s Honor by 1. As with other ability scores, a character’s Honor can’t exceed 20 or fall below 1.