Shared lists in Reminder got a nice upgrade in iOS/iPadOS 14. We can now assign people to tasks, and it’s easy to see who is responsible for each task at a glance.
To assign someone to a task in a shared list, tap the task, then tap the people button in the toolbar that appears.
To start sharing a Reminders task list, tap the (…) button at the top of any list, then tap Manage Shared List.