You can assign tasks to any member of a shared list, including yourself.
To assign a task within a shared list, open the task’s detail view and click or tap Assign. Then, select the member of the shared list you’d like to assign the task to.
Assigned to Me smart list
To view all of your task assignments, click or tap the Assigned to Me list. Any task that has been assigned to you will automatically show up here along with assignments from other enabled connections, such as Planner.
You can turn on your Planner connection in your To Do Settings.
The Assigned to Me list appears automatically. If you would like to turn it off, open your To Do Settings and set the Assigned to Me smart list to off.