If you are physically moving a trap or station that already has records associated with it, then you should “retire” (edit and select the retire flag) the trap or station and create a new one in the new location. That way the old records are correctly tied to the old location.
The new installation can have the same name. The retired locations can be viewed by setting the "retired" filter in map views and report.
If you do need to adjust the location (you would normally only need to do this if the original location is because it is incorrect), then edit the trap or station and click the point icon:
You can then simply click a new location to replace the old one.