That can be an issue for multiprocess software, that name their processes individually/differently. For example, if you have a recent version of Firefox running, searching for "firefox", won't return any results at all. In ksysguard you were able to filter processes by everything (command, pid, ppid (along with its children), tty etc) which would solve this and similar issues.
The way you do this in the new system monitor is by using the Applications page. On that page, the "Firefox" entry will actually list all of its sub-processes when you click it and show the details sidebar.
I'm aware, however, if the user has to manage process trees over and over again to filter out information visually, you might as well remove the search field altogether, because it serves no useful purpose.