It depends what version of ServiceDesk you are using and there have been different ways to achieve this in the past including SQL Trigger on the pm_process table or setting the _ProcessRef attribute value via a BOO calculation in Object Designer. The trigger method came first, then the BOO calculation method took hold for a while, but then customers started reverting to the trigger method again so it depends where you fit in that maturity cycle.
If you get to 2016.3 or later you can now set directly in the product via a property of each top level object; for example for Incident Management:
I'm unsure if LANDESK provides scripts to change the process reference numbers/lettering. We did however use database triggers as mentioned above by Julian, the post below has some examples near the bottom of the triggers we wrote. We created new custom fields to hold the new reference numbers on the pm_process table and pushed the values from requests, incidents, tasks, and problems in to the new fields. In our case we were trying to allow sorting by reference number or breach time on the my groups workload and my workload list, technically you could give any naming convention you wanted since they are custom field without impacting the out of box fields.
So far we are seeing no database performance hit from doing this but there's always a possibility triggers could cause performance issues if the transaction count per minute./second is extremely high.
Reference this post Sort on Calculated Fields Workaround - My Groups Workload List