Okay, I see now that you are concerned about duration rather than location of residency.
The name change code sections in there entirety are located at:http://www.scstatehouse.net/code/t15c049.htm
There is no duration requirement ... the law simply requires that you file in the appropriate court based on where you live at the time of filing.
You will not be required to provide proof of residency in order to file the petition, though the issue could be raised if someone happens to file an objection to your petition. If that doesn't happen, you will probably not be required to prove residency at all.
If you do, there is also no statutory specification of what documentation is required. Therefore, normal proofs would be sufficient, such as a South Carolina driver's license or identification card ... or perhaps a passport.
If you have no DL, ID or passport, you could any billing records which show that you receive services at the address (such as, phone, electric, water, trash, etc.), bank or credit card statements, or any other government or business records directed to you at your address.