@Sam Cook , To check SAMaccountname on Azure, you can login to https://developer.microsoft.com/en-us/graph/graph-explorer# with the same user by clicking on Sign-in using Microsoft button on the left and make GET call: https://graph.microsoft.com/beta/me/. In response look for the value of onPremisesSamAccountName attribute.
If you are logging in to RDP session using UPN, can you confirm if you are syncing onprem UPN as Cloud UPN or syncing email as UPN? If you are syncing email as UPN you would need to configure Alternate Login ID.