Nags are assigned to a Nag group, not a person. This is so that you have coverage if a particular person is away for example. A nag can only be assigned to a Nag group, but of course you can have a single person in the group. On a Nag, there should be an option to Assign the Nag.
So even though Nags groups are meant for multiple people there is nothing stopping you from creating a Nag group called <name> tasks or something and add them as the only access to the group (and yourself so you can view the queue).
A user can be part of all, some or none of the Nag groups. You can set the NAg groups that a user is part of in the Admin -> Users -> [select user] screen:
If a user cannot see any Nags, first check if they have been added to the Nag groups.
To see and change the Nag groups for a staff member, simply select in the modify user screen from above and view the Nag groups. In this example the user has no Nag groups. Simply click each Nag group to toggle each Nag group on/off for that user:
Note that support workers who only have the Support Worker App permission as "Required" and no other permissions, cannot be assigned any Nags because they only have access to the Support worker app.
