I am configuring Diagnostics & IIS Logs for Azure Websites. Azure Manage Portal shows options to store Application Diagnostics to Azure Table Storage:
This is apparently fixed in the latest (as of 3/21/2016) release of the Azure PowerShell cmdlets. You can now specify the table/container name, e.g.
Enable-AzureWebsiteApplicationDiagnostic -Name
Enable-AzureWebsiteApplicationDiagnostic -Name