You can rename a saved list from the Lists page or from inside the list itself. Both paths open the same "Edit List Name" dialog, where you can also change who can see the list.
From the Lists page
Go to Lists in the main navigation.
Find the list you want to rename. In the row for that list, click the Edit Details action (pencil icon). It appears as an inline icon button on the row, or inside the row's overflow menu.
In the Edit List Name dialog, update the text in the List Name field.
Click Save.
From inside a list
Open the list.
Click the options button (three vertical dots) near the top of the page.
Select Edit Details.
Update the List Name field and click Save.
Changing who can see the list
The same dialog includes a Visibility setting:
Everyone makes the list visible to all members of your organization.
Only me keeps it private to you.
Specific people... lets you pick individual teammates. You cannot remove yourself from the list.
Any member of the organization that owns the list can rename it. The Edit Details action is disabled for lists that belong to a different organization.