Are you 18+? If so, you can register your name for COVID-19 vaccination through any of cowin.gov.in, Aarogya Setu App and UMANG App.
Visit any of these three, and click on register/sign in. Add your mobile number and get the OTP (one-time-password). After receiving the OTP, type the digit number and click on 'Verify'.
Enter your details, including photo ID proof, name, gender, date of birth on the 'Register for Verification' page. And then confirm the appointment on the registered mobile number.