I'm not quite understanding what you are attempting to do, but my guess is that you are trying to use a PowerApps form to append to a temporary, in-memory collection (let's call this a dynamic collection). I haven't tried this, but I know traditionally you use a form to submit to a datasource's (for lack of better word) data source (e.g. Excel, SQL, SharePoint List, etc.). If it's failing, it's probably because the PowerApps form object wasn't intended to collect data into a dynamic collection.
What you can do is use a Collect command to append new records into your Names collection. For example, within a button's OnSelect property, you can do something like this:
Collect(nameCollection,
Table(
{
FirstName: firstNameTextBox.text,
LastName: lastNameTextBox.text
}
)
)
Now that I think about it, you don't have to scrap your form. Where my example says firstNameTextBox.text, you can just point it to DataCardValueXX.text. If you keep the form, you may want to consider resetting the form after collecting.
