Is there a way each tech in our organization can have custom filters in their "Group Ticket View"?
For example if tech A does not want to see tickets assigned to tech B but tech B wants to see all tickets, is this possible?
Not for the view, no. however, as a tech you could create an Advanced query to show just the things you want and save it. When you're on a view you can click on Query and select the query you made and essentially use that 'view' instead of the default of the Group Ticket View. You may have to do that each time you go to that view page though if you really only want to see the query data.
As kellytice said, no.
But if my Feature Request ( ) can gain some more ground and be implemented, then it should be similar to what you are looking for.