I understand that you are happy with the custom keyboard layout you made, but that you just want to change its name?
Then the easiest is to open it in Ukelele and change its name there with the command Keyboard / Set Keyboard Name and Script, then install it with File / Install / Install for Current User.
When you activate the new layout, you can also deactivate the old one, so it doesn’t show up on the Input Sources menu anymore.
You don’t have to delete the "Italian Copy" file, because it really doesn’t matter if it’s still somewhere on your system disk!
I say this also because there are several places where you could have put the layout, and one of them is normally hidden: In the Finder, you need to hold down the Option key while selecting Go / Library to go there.
So if you’re not comfortable doing such things, just forget about it :)