How i update a variable inside my widget blueprint from my blueprint actor and make it to work even if blueprint actor have more than one copy (instance) in the game?

If you just want the text to be displayed on trigger event of every door, then you can do it without using arrays too.

  1. Create a public variable for name of your door whose value you will set in level editor (Like you are doing now).

2)Create a string variable in your DoorWidget too.

  1. Set a trigger box for this Door BP on whose overlap you will set the value of DoorWidget variable using the widget reference(widget reference created while adding widget to viewport)

  1. Add a TEXT component in your widget, and create binding to it. Return the widget variables value in it.

It will print name on widget , everytime player goes into triggerbox of a Door BP

-AB