Such juggling isn't technically super difficult. The only problem is how to make it clear in the UI what is happening.
I understand you go to rename a slot, it says no, the name is already used. So you have to cancel, go find it, rename it, then find your first slot (page down) and rename it like you wanted in the first place. That is indeed a pretty terrible workflow and we could think about how to improve it.
It's not necessarily a "name swap". It might be confusing to give the conflicting item the old name of the just renamed item.
Maybe instead of the "this name is in use" dialog, when you try to set the name and there's a conflict, the rename dialog changes to show 1) the item you are renaming, and 2) the other item that has a conflicting name. each has a textbox that contains the same name, allowing you to set both names at once.
I've never seen other software do this, though that doesn't mean it's a bad idea necessarily. We just need to be sure it's not confusing:
Name: _____________
[cancel][ok]
Then:
Name: _____________
A slot with that name already exists:
Name: _____________
[cancel][ok]
I'm not sure it's immediately apparent the dialog is renaming both. 🤔