Inverse Loyalty

Regard?

Esteem?

Acclaim?

Dominance?

Sway?

Control?

Presence?

Mastery?

Honor
Leadership
Charisma
Fame

I'd say you could use good ol' Charisma or Leadership, as per the suggestions above.

However, Zag24 raises a good point. It looks like commanders with a higher 'inspired loyalty' end up succumbing to low morale faster. If you want to keep it mechanically the same, you could change the morale mechanic to 'Discipline' and the inspired loyalty attribute to 'Laxity'. That way, a higher Laxity score translates to a more negligent commander whose army is prone to becoming undisciplined.

You can get exactly the same result by choosing the right threshold and expecting people to add and compare. If you had originally planned on starting morale at 8 and lower-is-better respect at 3, then your starting state is that 5 points lost on them combined leaves them tied. Then just start with the same numbers (morale is 8, higher-is-better respect is 3) bur say that the threshold for mutiny is morale plus respect < 6. This gives the same result, but isn't going to confuse the issue when you say, "Give your men an extra ration of rum to raise morale" and "Charge boldly into battle to raise Respect." With your lower-is-better approach, you have to say, "Charge boldly into battle to raise Respect (which means lowering the value by 1)."

You could just use a track with two counters. I'm doing something similar for a ship combat game I'm working on. I have a track that the player has two counters on; one for morale, one for ship damage. In my system they each start at opposite ends of the track. As you take damage to one it move it. If they ever cross the crew surrenders. Of course my system works because I only have to have one track per player. If you are using multiple commanders per player it may get tedious.

Seriously, I know that you're kidding, here, but it's a very easy trap to fall into -- to blame the user when they get confused, just because something seems so easy and obvious to you. You forget that it (By it, here, I'm referring to the point that Respect is lower-is-better) is just an easy detail to you that makes sense because of how it is used. However, to a user, he doesn't yet know how it is used, and it is one of hundreds of tiny details at an equivalent level of importance that he needs to remember to start playing, and some users will forget. It doesn't mean they are not smart enough, it means that they focused on something else at the time that rule was mentioned.

I GUARANTEE that this will happen within the first 25 times this game is played by playtesters seeing it for the first time: Someone will do whatever action that increases Respect and he'll move the marker/token one higher on the Respect track. He won't realize that he's moved it the wrong way until a couple of rounds later when his morale goes down and suddenly his troops are abandoning their posts. He'll be puzzled and annoyed until he realizes that "Respect is scored backwards." (I'm quoting him directly, here.) Maybe his opponents will let him retcon his mistake, or maybe not.

Most users will blame themselves for the specific event, and won't mention it. However, their opinion of ease-of-use will go down somewhat, and they won't even know why they think so.

I apologize for going on at length here. I design software for a living, and I run into this sort of thing all the time in the software world. The developer does something for a good reason, to him, but users find it confusing. If his response is to blame the users (which is frighteningly common), then he has made a terrible mistake. Don't be that guy.