Task completed (only) by a specified user

I understand that the column "Assigned to" is mainly used to "assign" the task to a person to lately be able to calculate this person Workload.

But is there any way to specify that a row/task, can only be completed by a specified person (licensed or not)? I dont want that anyone, any participant, can be able to "complete" a task if this person is not the one specified in this Assigned to column.