The new OneDrive client is just OneDrive. It’s a unified client called Next Generation Sync Client. You should install the latest version of OneDrive downloaded directly from onedrive.com and it can connect to both personal OneDrive accounts and business accounts.
There is an old OneDrive for Business client still available known as the Groove client.
There are some limitations in the next gen client, if you want to connect to SharePoint libraries. But if you are just syncing and sharing file to Office 365 or others, the next gen client works great. It also is installed by default in Windows 10 and is updated shortly after a new user logs in, automatically.
Now, what you are asking for is seamless single sign on. Good news for you is that the next gen client just recently added the feature to be able to do this.
Two things are required.
Enable ADAL with a registry tweak:
Enable the Silent Account Config group policy:
You should read the above link, because there are additional group policies required for a completely silent and automatic configuration of OneDrive. The link will tell you how to obtain and use the latest group policy templates.
Microsoft is doing a great job on the Next Gen client and I’m thrilled to finally see this feature. Just one year ago OneDrive was useless. Now it’s fully capable of handling our cloud storage and sharing needs.
We’ve been using it successfully for at least a month or two now. New users sign in and OneDrive is up to date and ready to go without a single prompt to the user. Coupled with folder redirection we no longer have to worry about users storing data on their computers.