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 and put in the new. This can take some time, but will eventually happen and is out of our control.
You can speed up the process by resubmitting your sitemap to Google as this may get the spiders to your site sooner. 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.