Thank you for posting your query on Microsoft Q&A, from above description I could understand that you are looking for advise on does Entra ID display name of device changes if the device name is changed locally.
Please do correct me if this is not the ask by responding in the comments section:
Device name does not get updated after registration. The device registration service does not export the name once device is registered.
Only way to have common nomenclature for a device us by having it enrolled to Intune and deploying device rename template or rename manually via Intune.
OR
You may try using Set-AzureADDevice to update the diplay name property via Powershell.
Thanks,
Akshay Kaushik
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