For a business that does multiple projects for the same client it would be beneficial to be able to see and sort all of the projects under one client name.
When adding tasks there would be a section that would allow you to specify ‘Client’ similar to the projects section now
Your projects could be hosted under a team for this client. You can also have a custom field with the client name. The field would be part of a portfolio. Then through search and/or reporting, your would be able to see projects per clients.
Not sure I understand your last sentence. Don’t you have a project for each client? Why do you need to give the client name at the task level?
My go to for bundling projects together is by using portfolios. This helps with reporting also.