fixed lable function

Do you mean you would like to get a tooltip on hover only?

Instead of showing the point label as a popup, I want to display it directly on the map.

This works with marker only:
[leaflet-marker lat=28.41 lng=-81.58 visible]Marker[/leaflet-marker]
For leaflet-geojson you can use [hover] to show a tooltip on hover. The content of the tooltip is the same as of popup.

Can I add the name of the point in the Geojson file?

Example

Of course. Do you have an example of one point in your geojson file?
Its property should look like this, see https://en.wikipedia.org/wiki/GeoJSON:

{
      "type": "Feature",
      "geometry": {
        "type": "Point",
        "coordinates": [102.0, 0.5]
      },
      "properties": {
        "prop0": "value0"
      }
  },

Then you can write:
[leaflet-geojson src="my.geojson"]{@prop0}[/leaflet-geojson]