Support. There's tons of alternatives to the default in-game moniker for unnamed lore wolves, and people who don't care can simply not name their pups before selling and this change wouldn't affect them at all. So I don't see why a ban would be a burden on players.
But for players that do care about offspring lists, the ‘one easy step’ they can take to avoid the issue is currently reversible. The workaround of avoiding trading entirely has the unplanned effect of reducing engagement with the social parts of the site which is a net negative. Since wanting to avoid unnamed wolves in offspring lists is a common sentiment, the possibility of it becoming a vector for retaliatory action is an unfortunate possibility, and the moderation burden of determining the rare cases where it is a targeted action over an unintended one is not an easy task should the issue crop up.
The suggestion to have the option to hide an offspring list is a good one in and of itself*, but for the ‘unnamed issue’ specifically it's just a lick of paint and not a fix. Another option could be to change the formatting of unnamed wolves, instead of giving them the specific name of ‘no name’ they have nothing in the name space and it's formatted in a way that makes it clear that there's literally no name assigned, but that would probably overcomplicate things.
I guess my main take is the default in-game way of highlighting a wolf as not yet being named is not one that should be assignable by the player in my opinion. Since the game currently uses an actual name ‘No Name’ to signify this, then I don't think that should be a name that's assignable by the player. If the default in-game way was just a blank square or something then I'd be arguing that a player shouldn't be able to reverse a named wolf back to the blank box state.
*Seriously I like this idea a lot. Especially for when offspring lists start getting real long. If this is ever made as a separate suggestion post, poke me and I'll go put my support for it.