I have installed and configured our Portal for ArcGIS and now I need to connect my ESRI Global account user name and password with it and my AGOL account (same as Global account).
I don't think there is a way to collaborate using public account of ArcGIS Online. You would require an organizational account for that.
What are you trying to achieve? If you want to copy content across accounts, you could use ArcGIS Online Assistant
https://community.esri.com/thread/190904-can-we-move-the-files-from-arcgis-online-to-arcgis-portal