You can run the below command to get the Display Name and the size of the mailbox only and export them to TXT file named result in the path c:\result.txt
get-mailbox -resultsize unlimited | Get-MailboxStatistics | Where {$_.TotalItemSize -Gt 1GB} | Sort-Object -Property TotalItemSize -Descending | Format-Table DisplayName, TotalItemSize >c:\result.txt

You can run the below command to get all the Mailbox info and export them to TXT file named result in the path c:\result.txt
get-mailbox -resultsize unlimited | Get-MailboxStatistics | Where {$_.TotalItemSize -Gt 1GB} | Sort-Object -Property TotalItemSize -Descending | Fl >c:\result.txt