There is a different way to change your name on your certificate of competency depending on the category that your certificate comes under. The two different categories of certificates of competency are:
A coxswain is also considered a low complexity certificate of competency although it requires a different process to change your name.
Links
[1] https://www.amsa.gov.au/forms/certificate-competency-application
[2] https://www.amsa.gov.au/qualifications-training/equivalent-qualifications-and-skill-recognition/equivalent-first-aid
[3] https://www.amsa.gov.au/about/fees-levies-and-payments/fees-services-certificates-competency-and-vessel-safety#coc
[4] https://amsa-agol.maps.arcgis.com/apps/webappviewer/index.html?id=56235e38813c4b9e90d130e62b6f590e
[5] https://www.amsa.gov.au/qualifications-training/sea-service-and-task-books/proof-identity
[6] https://www.amsa.gov.au/node/1527
[7] https://www.amsa.gov.au/forms/eyesight-test-certificate
[8] https://www.amsa.gov.au/qualifications-training/domestic-qualifications/guidelines-medical-assessment-near-coastal-seafarers
[9] https://www.amsa.gov.au/forms/certificate-medical-fitness-international-certificates
[10] https://www.amsa.gov.au/node/14991