We don't have a straightforward solution for this, but here's the workaround:
Add a formula in Airtable to detect whether the "Name" field is filled or empty. E.g.
Re-Sync your base.
Turn on Compute Mode.
Set the fields in the form to be conditional and let them only show up if the "Name" is filled. Select the formula field you just created as a condition.
This way the form will only have the "Name" field showing by default and users will be able to click compute or "NEXT" to load the rest of the form fields if the "Name" doesn't exist. Or the user will get an error if the name does exist already.