It is a minor mistake but 12th certificates are important for any jobs,exams and as proof documents.Since the application forms are online, you should not face any potential issues at the time of document verfication and face delays etc.
The process to rectify this would depend on whether your 12th is from state board or the CBSE.
There are stipulated guidelines regarding the time limit to apply for the name correction. Please check that from your local board (we do not know your city or state) or CBSE(http://cbse.nic.in/faq/revised_dob_name_corr_rules_2015.pdf)
FOR 12 CBSE
1. You need to have a correct name affidavit, this would be issued by the local Notary attached to the civil courts in your region.
Then you need to publish the correct name in one English and one vernacular newspaper. Please contact the local newspaper offices who would do it for a small charge. Both these are important before you apporach the CBSE board for name correction.
This link gives you the application form (http://cbse.nic.in/faq/MM%202016%20Duplicate%20Form.pdf)
This link gives you the guidelines (http://cbse.nic.in/newsite/dup.html#guidelines)
This link gives you the regional offices that you can approach based on your school location (http://cbse.nic.in/newsite/contact.html#reg).
For CBSE correction, you also need the school principal to attest the application form. The charges are Rs 1000.00 for name correction.
FOR STATE 12 BOARD.
Please gather your 12 marksheets and college records. Draft a letter to the principal of the 12th college from where you completed and forward it through the college principal to the 12th state board. Enclose the relevant documents and pay the fees. Usually, the board issues the new corrected certificate in 4 weeks time. Approach the administrative staff of the 12th college who would know the process and guide you within the college rules. If the college declines to help, then approach the 12th state board directly for help.