The ability's description states that the dragon retains its mental attributes, indicating that whatever form he takes, he still thinks like a dragon. Somewhere in his speech, in his mannerism, or even just in the way he thinks, will be clues as to his true nature. How carefully he hides those clues should be reflected by a deception check, as the dragon is definitely trying to deceive the PCs regarding his true identity.
Mechanically speaking, I'd have the dragon roll a deception check against the PCs' passive insight score. As no one is likely to be looking for these clues initially, so it would make sense to grant advantage to the dragon, as well as disadvantage to the PCs (or -5 to their passive scores). If the players are actively looking for these clues, however, have them roll a regular insight check instead of using their passive score.
If one of the PCs is a ranger whose favored enemies are dragons, he should have advantage on the check, or +5 on his passive score, as he's well aware of dragons' general behaviour. If his favored enemies are humans (or whatever humanoid species the dragon is posing as), the ranger should also receive these benefits, but success wouldn't directly point to a dragon. In other words, the ranger's familiarity with humans allows him to detect that the creature in front of him is not a natural human, but not that it's actually a dragon in disguise.
As @Pierre Cathé's answer pointed out, the True Seeing spell would immediately reveal the shapechanger's identity. If the PCs are not high enough level to cast this spell, a Gem of Seeing would achieve the same results.
The 2nd level spell Moonbeam, available to druids and paladins, could potentially reveal the dragon. In principle, it would not, as the dragon does not have the "shapechanger" tag, but a lenient DM could allow it given the similarities between the dragon's shape change ability and that of "ordinary" shapechangers. Note that this spell requires a failed save to work, as well as dealing damage, so it's not necessarily advisable if you don't want to fight the dragon. The dragon can also use his legendary powers to succeed on the saving throw, but only a limited number of times. Moonbeam can be concentrated on and used multiple times on the target, meaning that eventually it would run out of legendary saves.