Let me start with a clarification. The names you see displayed in Elements Explorer, e.g. FirstNameTextBox, FirstNameTextBox0, FirstNameTextBox1, are the "friendly names". These are just names for us humans to read and identify one element from another. This name is not actually used during the test execution for finding the element. What does matter is what is the Find Expression for that element. This is what Test Studio uses to try and locate the correct element on the current page. We look for some unique attribute applied to all of the elements that are there e.g. the ID=CTL100_MainLink, src=\nextbutton.jpg, href=\page2.aspx, etc.
Without having direct access to your application, i don't know what it would take to easily automate entering data into the correctly row. It may be that you can always use the element FirstNameTextBox. Or we may need to resort to a few lines of code to find "the last row" and enter the data into there.
If you can give us more information, such as what does the HTML look like at the time the text needs to be entered, then we can help you figure out how to data drive this scenario properly.
the Telerik team