I'm trying to wrap my head around this.

As no one perfectly refrains from being memorable, children of honor die in dishonor. If a living person is willing, they can ritualistically take that dishonor as their own and through their own anonymous life expunge it. This is a matter of some responsibility, and a Child of honor would want to die knowing that they would one day be truly and properly forgotten. They would not want their residual dishonor to be passed on to someone who would in turn lead a dishonorable life.

Since their society does not lend itself to getting to know one another, the only way to establish that level of trust with someone is to raise them from an infant or a small child. Of course said child will remember you very well, So one of the rules you instill in them is that they do not talk about you.

Which is all to say that asking Children of Honor about their parents is even worse than asking their name.