I use a trackpad rather than a mouse, but the click pause click still works for me every where in Catalina (10.15.6). However, it is "touchy". Too quick and it is taken as a launch command. Too slow and it is sometimes ignored. As a result, I generally "right click" (Control+click) and use the context menu to change a name.
If you want to customize your mouse sensitivity (or keyboard, or trackpad, or touch bar and/or create mouse gestures, actions, commands,
etc check out
BetterTouchTool.