As of Aug 2018 it’s not possible to rename an Azure automation account, but this is the next best thing.  There are number of limitations to this approach, including the requirement to recreate schedules and a number of other automation account settings and configurations, but if you have a simple setup it’s worthwhile.

• Bulk export the runbooks from the incorrectly named automation account using the Export-Azure RmAutomation Runbook PowerShell cmdlet.
• Create a new automation account with the desired name.
• Bulk import the exported runbooks into the new automation account using the Import-Azure RmAutomation Runbook PowerShell cmdlet.  Use the -Published switch to save time having to manually publish each runbook post import.
• Recreate and link any schedules and other configurations.
• Import any modules required by your runbooks.
• Update the existing modules as they’re not the latest available when you create the account.