This would be a query for the next SSC exams. You have received different answers. If for example, I'am applying, when it comes to crucial documents and government process, there should not be any chance of me losing the job just because I had issues at document verification. So it would be advisable to keep everything in order rather than taking a risk.
The online registration for SSC-CGL Staff Service Commission - Combined Graduate Level examinations for 2018-2019 as expected to start in March 2018 with the last date to apply being around second week of April 2018. All these online applications have to be done carefully, doubly checking every word with respect to names,date of birth etc.You cannot change after entering and submitting the application.
If you have documents that do not reflect your mother's name correctly, now is the time correct the name so that it matches in all the documents that you would have to submit ultimately after the written test, when they come for document verification.
My suggestion would be to get an affidavit with your correct mother's name and then approach the 12 board via your school and the university via the college to rectify this in the certificates and mandatory documents which you will be submitting at the time of document verification. Anyway, this is what I would do in your situation.