When I search google with my name. Site by person A comes up in the search result. But the page does not contain my name. How can I remove this site from the Google search result?
You can't. For some reason Google has determined that this relevant for searches for your name and that page should be shown when users search for that site. The text a user searches for does not have to be on that page for it to rank well (although it typically is and usually is very helpful). Off page factors such as anchor text if incoming links can influence a page's ranking.
Your only chance is if that site/page is using black hat techniques to manipulate the search results. In that case you can reprt them to Google who then can respond by removing that page and any other pages that violate their terms of service.
I can't always tell whether content has been removed or updated. If you're sure the original content or image is no longer live on the page, follow these steps to remove the outdated copy of the image:
- Visit the web page that contains the content or image.
- Copy this URL it.
- Paste the URL of the page in the box below >> click Request Removal