Tiaral

I am more inclined towards the second point. As I see it, it is better suited to the character's goal. The first one is more for those who are driven by ideals.

I would say, the first one is for the fourth and fifth, and the second one is for the third.

That's exactly what I had in mind. I'm all for it. However, the fourth option isn't that bad either.

The main advantage of the fourth option is that it expands the list of quests that are suitable for us. We can also combine them somehow, though. The leader can follow personal ambitions, while the rank-and-file members of the order can be told something more appealing to them.

I had an idea to call ourselves the "Knights of the Gauntlet."

I don't see any obstacles. Moreover, it's a good option if this sacred symbol is somehow connected to the character's background or the history of the order.

It's funny that you mentioned that. I was just about to do something like that. A minor aristocrat, descended from a once glorious and great lineage. He was raised on stories about his ancestors who accomplished great deeds. And his personal motivation for seeking power and glory is precisely the desire to restore the greatness of his family.

That will work well. It's concise, clear, and quite ideologically sound.

Added 9 minutes later

And, in the event of the leader's death, there will be no particular problems with someone else taking over the leadership.

Yes, and I don't see any problems with the order either. Unless too many people die and only those who are very far from the idea of the order remain. But in that case, they will simply be reclassified as mercenaries, and we won't lose much.