Creating point at line end using QGIS

In the Processing Toolbox use the Extract Specific Vertices tool, for the Vertex indices use 0 for the first vertex and -1 for the last vertex. Which one you need will depend on the direction of the line.

EDIT: Apologies, I didn't read your question properly, you said automatically. If it's just for display purposed you could use a geometry generator symbology to show a point at the end of the line using end_point($geometry) as the expression. If you need to create an actual data point automatically every time a line is created then I'm not sure how to do that.

A simple solution could be:

Using Vector ‣ Geometry Tools ‣ Extract verticas. Afterwards simply delete all points but thoose which were generated at the end and beginning.

You can use the processing tool "Geometry by Expression" and either use start_point($geometry) or end_point($geometry) as expression.

If you want them for display purposes only, you can use these expression within layersymbology and add an geometry generator.

Additionally, I may suggest using PyQGIS, tested on QGIS 3.10.4-A Coruña.

Let's assume there is a point layer "lines", see image below.

Proceed with Plugins > Python Console > Show Editor and paste the script below

# providing the polyline layer's name
layer_name = "line"

# accessing the line layer by name
try:
    layer = QgsProject.instance().mapLayersByName(layer_name)[0]
except IndexError:
    raise ValueError("The layer {} does not exist.".format(layer_name))

# creating an empty point layer for output
point_layer = QgsVectorLayer("Point?crs={}&index=yes".format(layer.crs().authid()), "End Points", "memory")
provider = point_layer.dataProvider()

# detecting layer wkb and wkb type
layer_wkb = layer.wkbType() # integer
layer_wkb_type = QgsWkbTypes.displayString(layer_wkb) # string

# checking geometry type of the layer
if layer.wkbType() == QgsWkbTypes.MultiLineString: # getting end points for each part of a MultiLineString layer geometry type
    print("Your layer is a {}-geometry type".format(layer_wkb_type))
    for feature in layer.getFeatures():
        multi_geom = feature.geometry().asMultiPolyline()
        for part in multi_geom:
            end_point = QgsPoint(part[-1])
            f = QgsFeature()
            f.setGeometry(end_point)
            provider.addFeature(f)

elif layer.wkbType() == QgsWkbTypes.LineString: # getting end points for a LineString layer geometry type
    print("Your layer is a {}-geometry type".format(layer_wkb_type))
    for feature in layer.getFeatures():
        geom = feature.geometry().asPolyline()
        end_point = QgsPoint(geom[-1])
        f = QgsFeature()
        f.setGeometry(end_point)
        provider.addFeature(f)

else: # other layer geometry types are not accepted
    print("Your layer is a {}-geometry type, when only 'LineString' or 'MultiLineString' is accepted".format(layer_wkb_type))

# adding a new layer to the map
QgsProject.instance().addMapLayer(point_layer)

Press Run script and get the output that will look like

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References:

• Can vector layer get start point and end point of line using PyQGIS?
• First and last point of MultiLineString-objects in QGIS 3

Another approach via RMB > Duplicate Layer.

Then for a new layer by means of "Geometry Generator" apply RMB > Properties > Symbology > Geometry Generator as Point/MultiPoint. This will be for display purposes only.

If you are using "Geometry by Expression" from processing toolbox this is not for display purposes only. It creates the geometry as new layer.

Another example using pyqgis:

layer = iface.activeLayer()

def find_endpoint(feat):
    for item in feat.geometry().vertices(): #https://stackoverflow.com/questions/2138873/cleanest-way-to-get-last-item-from-python-iterator
        pass
    return QgsPointXY(item)

ends = [find_endpoint(f) for f in layer.getFeatures()]

vl = QgsVectorLayer("Point?crs={}&index=yes".format(layer.crs().authid()), "endpoints", "memory")
provider = vl.dataProvider()
for e in ends:
    g = QgsGeometry.fromPointXY(e)
    f = QgsFeature()
    f.setGeometry(g)
    provider.addFeature(f)
QgsProject.instance().addMapLayer(vl)