What is the correct way to handle libraries?

I had a Grove Temperature and Humidity Sensor V2.0 (DHT20) and I ran into an old topic from 2022 in this Particle Community adressing the Library needed for this device (<DHT20 (replacement for DHT22) Library>). The topic ended with a solution as proposed by ScruffR to copy an app to Particle Web IDE from the shared apps in: Particle Web IDE
Which I did and that worked fine.
However: that copied app is now on my Web IDE under the very same name as it was in the shared apps (in this particular case: DHT_I2C)
Now if I want to use this DHT_I2C app as a part of another app, I follow that same procedure, resulting in several different apps in my Web IDE however with the very same name.
That should of course not be the case. What did I do wrong?

There is no good way to do this from the WebIDE, which is one of the many reasons you should use Particle Workbench instead.

There is no way to rename a project, so the only solution is to create a project from scratch with the same source files and same libraries as the original, manually.