How to modify a JSON file with Javascript?

I'm using Mapbox. When you click on a polygon the name of the person who lives in the city appears. But I want it when I click to rename the person in the JSON file.

map.on('click', function(e) {

var features = map.queryRenderedFeatures(e.point, {
            layers: ['counties']
        });

var feature = features[0];


          $.getJSON('features.geojson', function(data) {

              feature.properties.nome = "JUBILEU";

         });

$('#QuestaoModal').modal('show');


});

But the wrong way, it's not working