Hi @sakuraime , welcome to Microsoft Q&A forum.
Every time when we provision a new Azure MySQL Single Server, it creates a unique server in the universe of Azure regions. Hence it is not shared with any other customers who provision their Azure MySQL servers on Azure. As an example, when we create a new resource we need to provide the name of server and if we try to add the same server (which exists before), it would not allow us to create the resource and give an error like below:
Please let me know if this helps or we can discuss further.
----------
If answer help, please select 'Accept Answer' as this could help other community members having similar queries.