Uhh. Dragon-anything doesn’t really sound like an elven surname.
I’d hit up the random name generator and get something fire related.
Emberheart, Flamesong and Firestrider is what comes to mind.
We know of at least one Night Elf who has Dragon in her surname - Kera Stardragon, one of the Priestesses of the Moon from Warcaraft 3. But apart from that Dragon seems exceptionally rare thing in surname.
Depends on the elven origin, night elf, highborne, blood elf, nightborne.
All of them have their surnames derived from their nation and profession.
Example: A night elf would have their surname derived from stars, nature, night. Blood elves and Highborne usually have their surnames around Sun.