Hi krass,

re:
> To be honest, I didn't quite understand in the end: yes, I deleted the second name, but how
> to make my solid have only ONE name and not two? ((((

That looks like you may have something like a space character in the name instead of the name being totally deleted.

The sequence you want is:

#1 - click on the selection dot for the name you don't want.

#2 - click on the name line of the properties panel to bring up the "Edit name" dialog.

#3 - press either delete or backspace so the name field is totally blank. Do not type in any other characters.

#3 - press OK and the name should disappear in the scene browser.

- Michael