How do I make a formula or what widget would I use for it to automatically insert the client's name from a previous slide onto another slide?

You can use the Update/Calculate Field condition in order to copy the value of one field to another. Here's an example:

Here's the result:

For more details, please refer to this guide: How-to-Insert-Text-or-Calculation-into-a-Field-Using-Conditional-Logic

Hope that helps. If you have any questions, let us know.