Generating start and end points for LineStrings

You can use the GRASS tool v.to.points for this. Select node and adjust minimum distance.

If you have QGIS 3.4 you can use Extract specific vertices tool to extract the endpoints by inputting 0, -1 at the vertex indices as you can see below:

The tool is located in Processing toolbox -> Vector geometry -> Extract specific vertices tool.

The input is a polyline composing of several segments

Using the above tool with 0,-1 indices provides the endpoints only:

You can also use a Virtual layer (Data Source Manager > Virtual Layer) with SQL:

select id, st_endpoint(geometry) as geometry from lineshp
union
select id, st_startpoint(geometry) as geometry from lineshp

You can also use expressions start_point() and end_point() to create start- and endpoints of your lines. Use this expression to get both at once:

union (
    end_point ( $geometry ),
    start_point ( $geometry )
)

Paste this expression on an additional symbol layer on your line layer to create points for visualization purpose only (see screenshot) or create a new layer with actual point geometries using Menu Processing / Toolbox / Geometry by expression and using the same expression.

Use these expressions in the attribute table:

• x_min($geometry)
• y_min($geometry)
• x_max($geometry)
• y_max($geometry)

As easy as that.