One of the downsides of anonymity that many people raise (fallaciously) as an argument against it is that too many of the anonymous people are just trolls, therefore it is a negative quality. Having it be people that are known to the person brings about an assumption of character that can solve this issue, so long as the user associates with people that they tolerate (which is a mostly fair assumption, considering how private groups and similar functions operate on the established platforms).

One problem that I could see is that someone could be found out simply by virtue of being the only person that would say something like them. I guess this could be alleviated by filtering in public posts from others, but this could cause other problems while not solving what it's supposed to.

The other issue for this is the Gab problem, which cannot be easily solved: that if you're using this service, you're a bad person who needs to be blocked/fired/etc. Unfortunately the mobs you're working against work to destroy with little rhyme and no reason, and they work for free (often literally unemployed). This problem is hard to get around, but I think could be mitigated with marketing it as a platform first and a solution second.

Nonetheless, I wish you the best. This is a very interesting concept and could really do a lot of good in the world.