How can I calculate and store a Core.Name to also use sequencing?

Summary:

I want to have EDMCs suggest/populate the 5 digit longer Department Number in the Core.Name property. For example, DEPT_10101. However, it obviously should not derive an input of a department number that we already have in our hieararchy. Is there a way of not only deriving the Core.Name but also have EDMCS intuitive enough to scan the current hierarchy to make sure there are not currently any node with the same name? If so, it then moves onto the next available 5-digit sequence.

Currently we have users that are manually maintaining a list of unused 5-digit department numbers in excel. The EDMCS requestor has to currently collaborate with the department maintenance number person to get the next available department number.