Hi Arslan Amjad,
You can move your App Service and other resources from the old subscription to the new subscription within the same tenant without changing the name of the App Service. these are some steps that you can consider
Check that both subscriptions are part of the same Microsoft Entra ID tenant.
You need to move all App Service resources to subscription, including the App Service itself and any associated resources.
The destination resource or when you are moving to other resource group must not have any existing App Service resources.
when you are changing, the inbound IP address for the App Service will not change, allowing you to continue using the previous URL.
Make sure to delete and upload any TLS/SSL (Transport Layer Security / Secure Sockets Layer) certificates to the new subscription, as they cannot be moved directly. These certificates are used to secure your App Service’s HTTPS connections, and if they are not properly transferred, your website could face security warnings or connection issues.
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