BaseCamp does get the waypoint name from the map it is planned from.

Therefore if you planning a route in the way, using the route tool in Garmin BaseCamp (because you are creating is with via- points, rather than waypoints), there is nothing you can do.

The only way you can get around this is to create a route using waypoints and joining them together, then you can name the waypoint with whatever number you want to.

There is an exercise in the online resource taking you through this -

Log into the online resource > Courses > Garmin BaseCamp > Select Windows or Mac > Module 1 - Unit 7

I appreciate in that exercise we put the waypoints in using grid references, but you could use the waypoint tool (top menu bar). 
Then, do as the training video does join them all together. As you are creating a route using waypoints (rather than via points, as you are when using the new route tool), you have the ability to rename them - 001, 002, 003 etc


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