Upvote:4
If you click the 'i' info on the ESTA application when filling out names it says below:
In the First (Given) Name field, enter ALL names exactly as they appear on your passport in the First (Given) Name field. If a second or middle name is included in the First (Given) Name field on your passport, it must also be included here. This field is required to complete the application. If you have no first name, then enter the letters FNU which stands for First Name Unknown.
If your middle name appears in your 'first (given) field' on your passport then yes you have to give this.
Should your application be approved with the mistake, follow the advice below.
How do I correct a mistake on my ESTA application?
The only way to correct that type of error is to reapply and pay for new ESTA. You should be able to make a new application if your previous application was approved. Just go into the application system and click on "Apply" button. You cannot use the update function to make a change on your passport or biometric information. If your previous application was approved, the system will not let you reapply until you close your browser after the first try. If you just applied, and are having difficulty changing something, try closing your connection to the Internet, and then opening it again. You might be told that an existing application is already in the system. If any biographic information in not correct, the application is not valid and you must click continue to proceed with the new application. Once you submit a new application, the old one will automatically be voided.
https://help.cbp.gov/app/answers/detail/a_id/1088/~/i-made-a-mistake-on-my-esta-application
Your application will not get denied for getting your name wrong, it may be taking longer to approve due to your name being wrong, remember it can take up to 72 hours to get an approval. If you get denied it's for something else; and it means you are ineligible for the visa waiver program and therefore an ESTA, you would need to apply for a B1/B2 visa instead.