Hello, dear developers.
Please bring back marker renaming behavior from version 12, with the floating ABC text input tooltip when renaming via double-click near the marker.
In the current version it is very difficult and inconvenient to find the exact boundary for renaming — instead, it often moves the playhead back to the marker position during playback. This makes marker editing unnecessarily frustrating.
Best regards
This is a new habit to get. You just have to double-click on the marker head itself and not on its side.
The old way was not very compatible with the new way of selecting a range by clicking and dragging on the ruler.
Note also that the double-click must not be too slow, because a single click on a marker head, without dragging, moves the edit cursor to the very marker position.
I posted this as a thread before, but my post was about why 2 options name and rename when both are working the same way. I see the name is changed to double click while the rename is still there. This is identified by the box being displayed on top for double click and below for renaming (on right click).
In Ableton, Reaper etc., markers are numbered. If you see the clip above, there is option to use a name or marker name is a number. In Ableton, there is also a shortcut Ctrl+R to rename marker which is useful. But for WL, I still do not understand why 2 options (Name and Rename).
May be, WL can have an option to write a name for the Marker or skip as in the clip above (without numbering) and have a shortcut to rename on clicking on marker head/when cursor is at marker.
I understand now — yes, it actually works quite well.
This behavior is probably related to me using a tablet instead of a mouse, so I likely just need to get used to it.
May I also suggest an idea? 
If possible, it would be great to have a keyboard command for renaming markers — for example, renaming the last added marker by the key command.
I know that WaveLab already offers several ways to rename markers, but this could still be a nice addition in my opinion.
In any case, thank you very much for the explanation and the response.