You can restrict the Assigned Staff column on a ticket to show only members of a group rather than the whole SharePoint list of users. This is done by going to Tickets/List Tools/List/List Settings, then the Assigned Staff column. Use the "Choose from:" option there. You need to choose a group (or you can create one for this purpose, such as Assigned Staff List).  

When you click the People Picker icon for Assigned Staff field on the Ticket, you get a short list of the names of whomever is in that group, rather than the full list of all SharePoint users.

Only members of that group show up in the box that opens.