Loot Log just does the icons (but why does LL do icons and not CK? because there are also icons for unknown set items and unknown collectibles, so instead of having icon-drawing code into multiple addons, I kept it in a centralized place in LL).

The order of characters is determined by the LibCharacterKnowledge settings, which you've found.

So the ordering first sorts by "Priority Rank", and then for characters that have the same "Priority Rank", it'll sort by age, from oldest to newest.

By default, everyone has the same "Priority Rank", so it's basically just sorting by age. For most players, their oldest character is usually their "main", so this provides a decent default out-of-the-box experience for most players.

But for me personally, my oldest is not my main, so the way to override is to change the "Priority Rank". You can set a "Priority Rank" at the account level and/or at the character level.

I think the best way to illustrate this is with an example.

So let's say you have two accounts, which we'll call "Main" and "Alt". By default, everyone has the same Priority Rank, so the order is by character age, which looks something like this:

Main-1
Main-2
Alt-1
Main-3
Alt-2
Alt-3
Main-4

Since both accounts have the same priority, it's done by age, and if some characters on the second account are older than some characters on the main account, they'll come first.

Now let's change the alt account's priority rank to 60 (you can set a number from 1 to 100, and the default is 50), leaving the main account at the default of 50.

Now the order looks like

Main-1
Main-2
Main-3
Main-4
Alt-1
Alt-2
Alt-3

Now let's say that your main character on your main account is actually the second character that you created, not the first, and you also care a lot about the main character on your alt account. Now you set the Priority Rank for "Main-2" to 10 and the Priority Rank for "Alt-1" to 20, and now it looks like this:

Main-2
Alt-1
Main-1
Main-3
Main-4
Alt-2
Alt-3

Where the main characters of your accounts are sorted first, followed by the remaining main account characters (sorted by age), followed by the remaining alt account characters, also sorted by age.

You can go through and give every character a manually-set Priority Rank if you want to have very precise control over the ordering, but I think that's rather tedious, so I personally keep everyone at the same default rank and just manually set ranks for specific characters that I want to promote above the rest.