Renaming components directly from the structure panel is possible only at first level, it's not possible if the component is at a deeper level. See picture...
Visual Studio Code 1.64.2 - macOS Catalina 10.15.7 - TMS WEB Core v1.9.5379
I retested this here but could not reproduce this.
Is this happening all the time, i.e. also from a new project?
Yes, it's happening all the time, also with new projects.
So far I have experienced this on macOS - not tried yet to use VSC in windows VM.
Hello,
I have been trying to reproduce it, but I couldn't, so I should be doing things in a different way, please, would be possible for you to record some kind of video with a simple set of steps to reproduce the issue? That way I'm sure I will be able to reproduce it and fix it, thanks!!
Hello Jose, have you received my email with details?
Hello Jose, I guess the email I sent on 23/FEB while traveling on a train got lost (there was a link to a video showing the issue).
I have good news today: yesterday after having upgraded all the modules in visual studio code under macOS Catalina the "renaming issue" is not present anymore 
At present I'm having TMS WEB Core 1.9.75493 (auto updated by VSC) and I see that versions 1.9.75486 and 1.9.75482 were distributed about one week ago... I guess you made some fixes!