Hello @JamesFyffe
There's only a couple ways you can apply a filter to view particular students in your gradebook and not the entire class. Of course, you can also view individual student grades this way:
https://community.canvaslms.com/t5/Instructor-Guide/How-do-I-view-assignments-or-students-individual...
Besides that, you can use the search for student feature like you have, but if you leave that page and move on to a speedgrader for example, pressing back is going to reload the entire gradebook. Your best bet is to keep this gradebook view with a few students open in a tab, and then right-click on things you want to view and "open in new tab" When you are done looking at an assignment or speedgrader, simply exit out of the new tab and your current filtered gradebook willstill be in tact. Besides these options, you'd need to filter with the built in options i.e. by section, assignment group, modules, etc. This would probably be more work and you'd have to move your students around to their own sections. Here is the Canvas guide:
https://community.canvaslms.com/t5/Colder-Storage/How-do-I-move-students-between-sections/m-p/174670
If you have enhanced gradebook feature enabled, there is an option for this built in:
https://community.canvaslms.com/t5/Instructor-Guide/How-do-I-create-a-filter-in-Enhanced-Gradebook-F...