In the Azure AAD portal under Audit Logs we are able to view a part of this info (the field is called Initiated By)...however there is no way to add the Department-property in that UI report. Powershell to the rescue then? :)
I like to know this as well. We need to track who invited a guest user to tie the guest user to a person who is responsible for the guest and help him with problems an questions, so that guest users don´t hesitate the IT-Support staff.