Hello hotport,

Try View > Show Attached Waypoints/Routes/Tracks, make sure it's checked.
Also perhaps View > Show Labels and View > Outline Labels.
I always use the .gpx format for any waypoint files I want to view etc. and it always shows their names.
There does not have to be a map loaded for waypoints to be displayed.

If there's too much clutter and many other labels cover them you might have to reduce the font size of the labels, remove some items from the map or zoom in to a level where they are visible.
Get to the font size setting by going Tools > Options > View > Font.

Sometimes GPSMapEdit will not show labels of some items until zoomed in closer, even when it appears there's room for them at higher zoom levels.
Though that seems to happen mostly with river and creek section labels, sometimes road or track section labels.
Any waypoints I display usually always show the labels regardless of zoom level.