Create a user-defined palette section (see "Edit" -> "Manage Palette").
Create an edge, style it as needed, add a label, and style the label as needed.
Right-click the edge to open its context menu and choose "Add to Palette".
Go to your user-defined palette section and double-click the template corresponding to your edge. This will make the new template the default style for edges. The template background should change to a dark blue to signal the change.
Now, when you create a new edge using the mouse, your template (including its label) should be used.
The palette might actually display the new template without its label depending on the actual "Placement" used for the label. Due to the small visible area reserved for templates in the palette, the label might be outside of said visible area. For "Placement" settings such as e.g. "3 Pos Center: Target Center", the template's label will be in the visible area.