Guy. You should not have this issue

on the “cloud” there will be no workstation, unless your customer is also planning to have virtual desktops workstations running in the same cloud environment, with your server where your app is running. But this scenario is not likely the common use case.

As I said earlier, the users will have to connect remotely to the server in the “cloud provider” using RDP. This will open a remote session on the server for each user. Your server must be licensed ( remote CALs) to allow N rdp sessions.
And you can configure the server to allow only one single session per user. The user will normally belongs to a windows domain, so no chance of having duplicated user names.

If you give more details on how your “cloud” environment will be, Others that have worked on this will be able to assist.
I have never done this using recent cloud providers, but have done a lot of df deployment on windows terminal services.

Regards and good luck