If you have recently deleted pages from your site or changed page names and they are still showing up in Google's index this is perfectly normal. It will take some time for Google to re-index your site and see that there have been changes. When these changes are detected, Google will remove the pages from their index. This can take some time, but will eventually happen. This is out of our control.
You can speed up the process by resubmitting your sitemap to Google as this may get the search engine bots to visit your site sooner and capture the changes. Please keep in mind that this method cannot guarantee quicker removal of deleted content.
The deleted content will also remain available like Google's cached pages.