Delisting
Delisting means a search engine stops showing a page in certain searches even though the page stays online.
How to request it
Google's personal information and legal removal forms, Bing's Report a Concern and the European right to be forgotten forms. See removal from Google.
Versus deletion
The page stays online and may appear elsewhere, so each search engine needs its own request and, where possible, the source is fixed too.
Frequently asked questions
Does delisting only affect searches of my name?
For right to be forgotten requests, yes; personal information and legal removals can remove the result from all searches.