You have filled your name wrongly in the online form BUT complete the document verfication. Looks like it is a spelling mistake and the verficiation authorities have overlooked it.
There is no need to unduly worry about this issue, you can join the department provided you update the authorities regarding the spelling mistake etc about your name. Only errors in date of birth, caste and age would be frowned upon, if it looks like you have modified it to fit the eligibility criteria.
Pleae check the application form and the document verification call letter for an adddress, a name or an email contact of an officer or authority related to the selection team.
You can just draft a letter
I so and so, had appeared for the written exam (date) and then had the document verification(date) done. I would like to bring to your notice about a small spelling mistake in my name. My correct name is so and so and I have enclosed attested copies of my identity documents with my correct name.
I request your kindself to note the minor error and help me to avoid further queries
Your name, the reference number for the job
Copy of the admit card for written exam
call letter for the document verification
the attested ID proof copy with your correct name.
you contact details.
Please keep the acknowledgement of the posted letter or email copy print out with you for future reference
You can also visit the website (http://ssc.nic.in/) to try and find some contact details based on your specific job advert.