Nobody does use the name, but Moiraine recognized the banner of LTT for what it was the second she saw it.

Whether the creature is known as Dragon or not is immaterial. In educated circles, people know the red-and-gold creature was the sigil of Lews Therin in the War of Shadow. So the question remains the same: why would Arthur Hawking put the symbol of the Kinslayer on his scabbard? He spent several years actually bringing down a false dragon - what could have possessed him to use the symbol of the Kinslayer himself?

Now, if that scabbard had a the golden hawk on blue, we'd be getting somewhere. But it hasn't.

Half the world is under Rand's protection now, and half the world is under Tuon, who has organized her half quickly and efficiently. The two should be 'as one' before the Last Battle. This is perhaps what the distorted story from the fourth age is about, not Rand having Justice, Rand and the Seanchan as protectors of the Light. Or, for all we know, the legends of the Dragon and Hawkwing with justice have been merged by that point - notice it has already distorted LTT's titles - not Prince of Dawn/Lord of the Morning, but Lord of the Dawn, and how Hawkwing's sword Justice is transformed into the sword of justice.