SSRS - Report folder name

If you select "Manage" from the dropdown list you posted in first screen shot you can see its properties and all you can do with that Folder including changing its name depending on the level of SSRS access your login has.
As far as a report not showing changes after deployment it could be that is also a permission related issue as in your case it seems like you're using new SSRS version so the reports do not need to be "compiled" before deployment like in older SSRS versions. There are some known issues with not showing some parameter values changes after redeployment but your case seems to be different however...if nothing works than removing the report and start with a fresh/new copy of it should always work however...this should be the last resort if nothing else works.

Thanks for your comments.

and all you can do with that Folder including changing its name

You see by default it is showing that name,i want to know where it gets this from.thanks

 

i want to know where it gets this

Do you mean you want to know who called it like that? Is most likely the person that created it OR last modified it and all that is under properties. If you rather mean "where is that name stored..." then have a look at the Report database in the Catalog table and more detail can be found here https://www.mssqltips.com/sqlservertip/3693/find-tables-columns-or-stored-procedures-used-in-a-sql-server-reporting-services-report/ about where SSRS report metadata is stored

Thanks for your comments

Do you mean you want to know who called it like that?

I want to know where the location where user enter this title, so I can edit it.