No Support Ever.
This comes up quite a bit, so it would be worthwhile to use the forum search.
The owner gets to decide what happens to the dragon. This includes genes, colors, exalted, and yes, named or not. FR has already outlined its stance on the issue
here. Once a dragon is sold, traded, or otherwise leaves a lair, it belongs to the new owner full stop. The new owner can do whatever he or she wishes with the dragon (excluding rule breaking).
So the bottom line is for breeders to name before they sell, trade, or otherwise relinquish ownership.
This extends to once the dragon is exalted. All exalted dragons are still tied to the accounts of the people who exalted them. The proof is when that player changes flights, all of his/her exalted dragons serve the new deity.
This isn't a matter of someone being lazy, rude, or inconsiderate. People have different play styles. Unnamed doesn't bother many people; they sell Unnamed so other players don't have to buy a Scroll of Renaming, and they accept that these dragons might forever be Unnamed. Others use it in lore. This includes Unnamed offspring (some players use Unnamed exalted offspring to denote stillborns) to Unnamed parentage (I have a couple myself, and I don't want that to change. At all.) Some players mass exalt so much that taking the time to name, or even use the randomizer, would slow down their Dom efforts.
Forcing names on people interferes with all these different playstyles. It ruins lore and handicaps exalting. If these names are randomized, it's even worse, as many people hate the names inside the randomizer.
This also fails to consider other names players dislike. Look at all the exalted dragons saddled with names involving "snot" or "fart." Should the owners of those dragons' parents also have a say in those terrible names? What about dragons that are Unnamed but in active lairs? In inactive lairs? This suggestion doesn't deal with those, which means anyone who sells Unnamed could forever wind up with Unnamed on an offspring list.
It's also unfair to let the owner of the dragon parents have control over the name. What if the two different players own the parents? What if someone bought an already bred dragon? What if the Unnamed dragons were bred and now have active offspring with Unnamed parentage? All of these scenarios ultimately boil down to trying to give control to someone who isn't the dragons' owner. And that just isn't how things work.
Forcing any type of generic or default name upon exalting wouldn't be well received either. If every Unnamed dragon got automatically named Acolyte, for example, upon exalting, people would just dislike it because it's the default name. The same would go for any default name assigned at hatching, sale, or exalting. That is what the root problem of Unnamed is. People dislike it because it's the default name, and that is something people will have to change their own mindsets about.
I do support FR creating a mechanic that lets players cherry-pick which offspring are visible or not. This includes exalted, not exalted, named, badly named, Unnamed, ugly, pretty, lore-relevant, lore-irrelevant, bred by another user, or any other reason a player may want to hide an offspring. Of course, there should be a link to the full offspring list for genealogy purposes and as an anti-scam measure.
I also like the suggestion of nicknaming dragons on your profile only. This doesn't actually change the dragons' names. It's outlined
here. I like this suggestion less than the cherry-picking offspring suggestion, but if that's what we get, then that's what we get. I won't complain because it's better than this suggestion.
Pings are disabled.
If writers are supposed to "show not tell," why are we called "storytellers" and not "storyshow-ers"?