Is there anything i need to check or like any settings changes need to be done? Because in some environments alone it is not working as expected

Yes i could see the page but the value alone is not getting updated.

yes am doing like this, but then too after clicking on adjust also the page properties is not getting updated only the components which uses that link is getting updated.

I changed the name of the assest in DAM and published it, but the assest name is not getting updated in the page property where it is mentioned. Please let me know on how can we achieve it?

How to update a page property field with the value of path to the asset which has been publish in author.