Hi G,
Yes, OneDrive and SharePoint Online both have the Version History where you can see the name of the person who modified the document. But if you shared the files individually in the OneDrive, you can't check the Version History of the shared files from the Shared tab. You need go to the orginal location of the document or file in the OneDrive and check the Version History.
Reference article: View previous versions of Office files.
If you need any further help, please feel free to post back to us.
Apperciate your understanding and stay safe!!
Best Regards,
Chitrahaas