Replication steps \(note: these are \*very\* precise; changing them in any way will not demonstrate the behavior\):
Zoom in on a trace consisting of a single segment so you can see the net name.

Select trace and copy.
Paste it somewhere.

iClick in Net, hit delete, hit Enter to clear the net name. The net name of the new trace disappears.


Click on the new trace. THIS IS AN IMPORTANT STEP. YOU MUST DO THIS. The trace should hilight mauve and the drag dots will be visible. If it does not do so, click on it again until it does.
It is only in this state that the anomaly will present itself.

Copy and then immediately paste the trace.
Click on the new trace. It will display a "null" net instead of an empty net.

The same behavior occurs when using cut instead of copy.
Note that if the trace is not selected to the mauve state, the anomaly does not occur. The cut and paste proceed correctly, and the new trace has a blank net name.
Best,
R
Chrome
80.0.3987.149
OS X
10_15_3
EasyEDA
6.3.22