Hi krass, it's possible to assign a name to face and edge sub-objects of a solid if those are selected when you set the name. That's what you have in your case here.

To clear those, click the selection dot area of the names that you don't want:


Then click on the name line in the properties panel here:


That will bring up the "Edit object name" dialog which looks like this:



Press Delete to clear out the name and push "OK", and that will remove those names:


re:
> But if I delete this name, the solid is also deleted.

You don't want to delete the objects assigned to the name, you just want to clear out the name property on them using the "Edit object name" dialog.

- Michael