Two suggestions:
Try exporting all contacts to a .csv, reorganizing, and then importing the contacts again. That way you can be more in control of which contact is assigned which ID.
On some printer models you can also switch the searching mode from "Find matches beginning with the search string" to "Find matches containing the search string". If you can find this feature and modify the search criterea then your printer should be able to find whoever you are typing in on the control panel.