If im not misstaken this procedure is somewhat like this :) (though i prefer cloud-only)
Azure-AD Object will be named after synced OnPrem object. Intune Object will be named after Azure-AD object on enrollment (can be changed manually). Name changes on Azure-AD Object should replicate, but i believe this will not change Intune object.
As you might be aware off, Intune does not use an "image". But if you would deploy an image via etc Software center you should make sure the existing Intune object is deleted before deploying again. Azure-AD object is fine... (The same scenario arrises if you reinstall via Windows USB-stick)
Autopilot objects are named after S/N. Once you start using Autopilot i highly recommend that you name everything by S/N otherwhise you'l go insane.
This is not a scenario i've tested. We avoid using Fresh start feature since it does not reconfigure policys applied on device lvl (cloud-only pc). "Fresh start resets the PC to an OOBE state" and then lets users sign in. Does not sound ideal for the situation you have..
rename is officially supported either through Autopilot for HAADJ or AADJ devices (for HAADJ iyou need Autopilot connector deployed and Domain-Join configuration profile assigned which will kicks in after HAADJ Autopilot done its job) or via remote actions but ONLY for AADJ devices.