The question wasn't about how to determine all truths, only truths about what things are named.
For example, a bridge was constructed in central London named William Pitt bridge, named for the Prime Minister. But people didn't _call_ it "William Pitt Bridge", people called it "Blackfriars Bridge", because they'd always named that part of London "Blackfriars" and that's where the bridge was. Today the replacement bridge is just named "Blackfriars Bridge", nobody bothered writing "William Pitt" and being ignored.
It is still named Blackfriars Bridge to this day, even though the adjacent railway station, named Blackfriars, is actually in the form of a bridge, crossing the same river, if referring to _this_ bridge people call it "Blackfriars Railway Bridge".
But even though consensus is the appropriate tool for figuring out what these bridges are _called_ we certainly shouldn't use it to figure out when they were built - what they're made of - which country they're in and so on.
There is no inconsistency, just a missing set of quotes around "right" - I hold there is no right or wrong in this matter. I don't reject the right of the people living in the area to try to influence the concensus - they might have even a financial stake in imposing "Lakeview Heights" over "East End Projects". But do they have a fundamental right to self name?
Seems a bit strange that you combined an absolute prescriptivist stance ('what's right') in support of an absolute descriptivist one.
It's not logically self-consistent: what if a consensus forms that your view here is wrong?