Hello and thanks for reaching out :)
Since the klaviyo integration was built by their team I would suggest referring to the following article here about integrating a typeform with klaviyo.
The short text field should be the correct question type to use for a first name field, just make sure they don’t have a length limit on that field for collecting names.
If the issue still persists after the typeform changes have been published and the attempt to connect to klaviyo fails, I would suggest reaching to their support team and asking about the compatibility of the short text question with their first name field.
Have a great day.