That is a Fighter, with a Noble Background. The very point that you are arguing that you need to have an entirely different Class just to be able to _lead_ simply undermines what the Fighter can be. As it does for all Classes in fact - why can't any Class potentially be a good leader? By artificially introducing a Class whose sole purpose is to _lead_ (regardless of whether other characters want to be led), you are undermining an essential roleplaying aspect of the game.
But a Fighter with the noble background does not do that. Or not enough to be worth mentioning. And once again, you are missing the point by being to literal in the 'leader' designation. There is nothing about the warlord that says they have to be the party leader. They just help the party by their inspiration and/or tactical acumen. They are the team assist leader, not the leading scorer, to use a basketball.
Moreover, as with a few posts, if your counter-argument to the point about a 'Warlord' being a problematic name is merely to list a bunch of other names with the implication that it does not matter what it is called, then it illustrates the point again that there really is no archetypal/narrative niche that exists for a Warlord. It's purely a game-mechanic inspired Class.
Because you don't like the name and it could be taken negatively in a game that is, essentially about a bunch of murder hobos? That does not make it a 'purely game-mechanic inspired Class', though game mechanics do have something to do with it.
Now, I made this comment last night before I went to bed, and immediately got a bunch of responses in response. To me, it indicates a somewhat fanatical aspect, obsessing over one Class. I'd suggest people would find more traction in trying to develop a strategic sub-class of Fighter to taste, rather than petition for the inclusion of a Class that was removed with entirely justifiable reasons given, after the most extensive playtest in D&D history. The Warlord is a done deal, no matter how much you petition for it's re-inclusion. My post is merely reminding some folks here, that have convinced themselves of one thing that there are whole bunch of folks who entirely disagree and simply aren't wanting to debate it any more.
Or it could indicate that your arguments were so spurious and edition warring that people felt they had to comment, even if they have said in this very thread (like myself and others) that they are not sure if a Warlord is needed in 5e. But yeah, fanaticism, that's it.