How to divide one existing trail into two parts

Hello, I would like to divide an existing trail into two parts that can each be named accordingly. I would rather not erase and redraw the trails since they are currently accurately mapped.

In iD, right-click a node in the way and hit the scissors.
But first left-click the way and check if it contains any relations. iD might screw up relations so then you’d better split the way in JOSM.

I use the ID editor