Add a written in option to a product

I'm selling t-shirts with personal names on the back. I need a way to let the customer type in a name on each item purchased. Maybe a box under each item that would say "personal name for this specific shirt". Is this possible? They might order 4 shirts if different sizes but only the meduim size gets a name.

You can do that by creating a custom field of the table "item" via the menu Display->Custom fields in the Business edition.

I have this setup but also. If a buyer chooses 5 and clicks "add to cart" It only gets one message. How do I get it to collect a message per item or hide the choice to add multiple items?

The easiest way is to hide the choice of adding multiple items.
You can do it via css:

Thank you. Looks like that would hide it for all products which is not really what I want either. Really would just like to have a custom field per product selected.

It's not possible to have one instance of custom fields per quantity of the product selected. (not unless you recode the whole custom fields and add to cart handling as well as a big part of the product page display...)
It's far easier simply not allow the user to add products to the cart more than one at a time when needed.

To do that, you can add the code: at the beginning of the file "quantity" of the view "product" via the menu Display->Views.