This is a "+" thread. That means that this thread is only for positive contributions about the Warlord. The purpose of this thread is to crowdsource a Warlord.
Taking you at your word in the OP:
Positives about using the Warlord as the name for the Warlord class:
Obviously, a big one is continuity with the original class and concept, as illustrated by the choice to use "Warlord" in the OP quoted above, twice. Warlord clearly communicates the concept and puts it immediately in the context of D&D, where it was a core class appearing in a PH1.
Warlord, like "adventurer," implies absence and/or defiance of authority, and the use of force (and other less polite means) to accomplish goals under difficult circumstances where civilized solutions are not always available. Warlords don't require a military hierarchy, officer's training school or the backing of a society with armed forces, they spring up, much like other adventurers, though, in their case, more defined by their allies than anything else.
The word is suggestive of the genre, both in the mere look & sound of the primitive-feeling portmanteau of War + Lord, and in it's usage therein.
Evokes specific fantasy and related-genre heroic characters, like John Carter, Xena, and DC's Warlord.
Similarly, another interesting one is imagery. Do a google image search for Warlord:
Pretty fantasy/D&D-appropriate