I'm assuming you have a parent list where you are running a workflow that is creating tasks that are getting assigned to different people. And that it's on this parent list that you are wanting to display the names of the people a task is currently assigned to. Is that correct?
To accomplish what you are asking, I would build the workflow on the task lists itself. Whenever a new task is created, or the assigned to field changes, you would run your workflow. Assuming the tasks were create from a workflow, they would have a Related Content field that links back to the parent. You could use that to query the parent list and find the correct item. To update your choice field, you'd need to get the name the task is assigned to, and then change it to match the values you have in the choice field. That will probably be the challenging part unless the choices are static. Once you have that, then you can update the parent item.
That being said, it may be easier to just direct people to the task list itself to see items they still have assigned to them? If the tasks are being created by the workflow, they already have a Related Content field that links back to the parent item. And the tasks are already assigned to the user, so you can filter your views how you'd like.