Generate input fields defined by dropdown

Somewhat, yes. Assuming you are using a drop down or radio buttons to select from a known quantity of clients. Then you can use conditional logic to show the correct number of name/address blocks. It will be somewhat tedious to set up, as you will need to design the form so that if they select 1, you show 1 name block.

Then, if they select 2, you show 2 name blocks. All the way up to 9 (or however many clients you allow in your drop down.) So, you will have 1 name block for 1 client, 2 blocks for 2 clients (in the drop down), 3 for 3 selected in the drop down, etc. You will eventually have 1+2+3+4+5+6+7+8+9 name blocks in your form.

It's not ideal, but it is possible.

Form fields are not generated on the fly. They're all pre-defined when setting up your form.

There are no trials available that I'm aware of. Gravity Forms can show/hide input blocks based on the value of a drop down, from 1 to 9, as you describe.