In short, no. IDs are designed to be a unique and consistent reference to a document for ever. They will be retained if you rename or move a document. They are 'internal' system generated ids used to create the various relationships between data tables. As such, if they are changed then all sorts of things will 'break'.

If you want your own IDs however you can create a document tag of your own and populate it with your own ID system (The system could also be programmed to populate these tags automatically using the plugins feature).