Not necessarily, I've found it unlikely to get someone to admit they are still a slave....that's an explanation/meaning/reason in itself - or as the saying goes, I freed a slave once, could have freed hundreds more if only they new they were slaves.

But as said, the issue on names has been done to death, enough for you to conclude as long as people are free within their own minds then people will be what people will be and will not know themselves until their backs are against the wall....if they're unlucky.