Thanks for this but I don't quite understand. Mapsource has a simple ticbox to tell Mapsource to keep the ascribed name and not create its own. Is that not there in Basecamp? I certainly haven't found it
When you have created the route in Basecamp
Give it the name you want by highlighting it in the bottom left navigation panel and right click and choose rename
Once you have done that keep it highlighted and click the transfer to device button in the top tool bar