I ran into an issue with a Powershell script I wrote recently, where I received this error:

The name must be unique per mailbox. There isn’t a default name available for a new request owned by mailbox xyz

Basically, a record is kept for completed mailbox move requests, and if you do too many for one mailbox, you get the above error. Don’t worry! Just run the following command in PS to clear away the completed request records, and you’ll then be able to run the import request!

Get-MailboxImportRequest -Status Completed | Remove-MailboxImportRequest

That’s it!