You can either update the connection string to explicitly have a valid username and password to log into your SQL server, or you can change the identifier that works in the DefaultAppPool program inside IIS.
For the first, you need to create a SQL Server login with sufficient access to your target database.
For the second, you should go to IIS => Application Pools => Default Application Pool => Set Properties => Process Model => Change the identifier in LocalSystem or your user input.
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