If you are using onedrive or any other cloud storage system is your identity safe when you connect and want to browse using a VPN or should you shut down all USERNAME / PASSWORD required services before using a VPN connection in order to remain anonymous?
it's a good question, especially considering that your browser's sessions are primarily saved as cookies and so the ip address you're coming from - vpn or not - doesn't really matter. As a particularly egregious example, take facebook links on sites. Those are loaded from facebook, which means you send them your cookie to then request them. So if you're logged into facebook, facebook knows every site you visit and yes, your Ip too.
So the answer is yes. To remain more anonymous on your VPN, you should only use incognito or private mode browser and never log into any identifying site that you also use without the vpn.