Dear google,

I recently contacted a newspaper institution to remove a certain name
in an article published on the internet. They agreed and removed it on
the website. Yet, when that name is searched on google, the original
article with the name is shown. Can this be removed? And is there a
time when it will be removed?

Although I'm not an official Google Researcher, this is what I found.

You might consider checking ://www.google.com/remove.html

According to Google, except in instances involving legal issues or
spam, Google's policy for removing a page from their index requires
that they obtain the permission of that page's webmaster.

Have the webmaster for the newspaper institution in question contact
them with proof that he/she is indeed the webmaster. This proof must
be in the form of a root level page on the site in question,
requesting removal from Google. Once they receive the URL that
corresponds with this root level page, they will remove the offending
page from their index.

Hope this helps.