It looks to me that once the link is corrupted due to name conflict, it does not matter if you sign in at another computer.
Try changing the name using the following, Settings/System/About/Advanced Settings/ComputerName. After restart, check Settings/Account/Linked devices and see if computer name matches.
One solution is to create a new outlook account and start fresh. For me, I will be loosing old Xbox games that I purchased so it is not a big deal. It will be a hassle to update my email address in my accounts. You can close the old account (30 days grace period). After grace period is over, try creating the email accounting using the same username.
Bro I have been resetting my computer regularly for 5 years. In my previous resets, it was visible even when I entered the same computer name or a different name. If something like this happens with such a simple name conflict, then I should not use Windows with my account xd All my social media accounts, game accounts, etc. are registered to this email address. Why would I delete my account and open a new one just because my device is not visible? Many things may not be registered to your account, but mine is?