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Try the portable version of:
Download AnVir Task Manager Free - MajorGeeks
See if that can identify the program.
I am not sure what you mean. It's Windows 10 telling me to update.
This Tutorial may help:
Tenforums tutorials | Hide or Show Notification Area Icons on Taskbar in Windows 10
I have updates disabled which is why I am puzzled why Windows is even monitoring it.
When I right click I get two options 'Check for Updates' 'Open Windows Updates' and I do not want to update because of the recent issues.
I thought that you wanted to know what the icon is. If it's an update notification then update. If you don't want to update have a read of this thread:
Stop Windows 10 Updates Properly and Completely Solved - Windows 10 Forums
Well, it's way past time you updated. From the position of your notifications on the left of the clock you must be using version 1511 (10586) or the original 1507 (10240). Notification moved to the right of the clock from 1607 onwards.
Support for 1511 ended over a year ago on October 10, 2017, 1507 on May 9, 2017. You won't have had any security updates for over a year.
Microsoft - Windows lifecycle fact sheet
Is there any good reason you haven't updated?