So, I’m creating a pre-selected list of names for the dragons. They will still have their default names, I’m still calling them by said names. The plan is to have nested choices discouraging customisation of the dragon names. So
I’ll admit I strongly dislike the idea of people calling the dragons by other names. It’s weird, they’re my characters and I don’t let you name any of the other NPCs. That said though, it makes sense you can name them, and hopefully that’ll give people a stronger sense of it being their dragon, and being attached to it. So I guess I won’t make the name choices complicated.
Anyway default names are planned to be
Fire Dragon: Sparky! Flame, Cinder, Ember, Blaze, Candle
Water Dragon: Aqua! Dewdrop, Lake, Ocean, Brook, River, Rain
Herb Dragon: Lilac! Lavender, Violet, Pansy, Chive, Foxglove,
Poison Dragon: Swampy! Bogwort, Marshy, Mushroom, Toadstool, Quag,
Song Dragon: Chime! Choir, Cacophony, Melody, Harmony, Symphony, Birdie, Ducky,
But with an option so you can name the dragon yourself. Just if it ends up as Spyro or Toothless, don’t tell me. 
Names are listed here so if you have any suggestions that are better than my own, please offer them. They should be thematic for what sort of dragon they are. And I likely won’t use all those mentioned above anyway.