After the above procedure once your in Thailand have your certified marriage certificate translated into Thai by somebody who is recognised by the ministry of foreign affairs as certified to translate. Then simply visit your local Amphur 'district' office they will issue a certificate in Thai and a Kor ror 2 document.
As an Australian passport holder I did not need to report back to the embassy after getting married. Should you need to show somebody in the US then have the certificate and Kor ror 2 translated by somebody certified by the ministry of foreign affairs
The ask:thailand community, consisting of multiple Q/A groups with over 100,000 members, powers this platform. It is not an official government resource. Our members actively contribute to this resource, and while we strive for accuracy, we cannot guarantee its complete reliability. Assistance to travelers is provided as a community service.