Do we have a way how we create groups?

We usually create different boards and then add people who are meant to work on that board. For example, if a team is handling requests from clients, then a board for client tickets is created and we have cards in it that represent one ticket. We can add the solutions team to that board and the person who is solving a particular tickets add himself to that card and the flow goes on right from backlog>>doing>>QC>>done>> up to close.