Hi,
From your description it sounds like you have one name per row and want to count the row instances. You can do that with the Instance Manager.
If you want to send the amount of rows to a NumericField for example. Add this to the Add Row button click event javascript:
NumericField1.rawValue = Table1.Row1.instanceManager.count;
Here is my test example:
The table row repeats, the button adds the row and count to the NumericField
