I am a NY lawyer. I would suggest having a lawyer do the paperwork -- like the deed, etc. A deed is very specific and you can buy yourself, or later down the road your beneficiaries, many problems if it is has errors in it. Don't be penny wise and pound foolish.
SC as in South Carolina, Suffolk County or Supreme Court? And what do you mean by name change on your deed? Is there a mortgage on the property?
After answering those questions you should check with the relevant clerk to see what you'll need - and if you have the documentation, you can decide whether you're comfortable with the procedures.
As always, do not construe posts as legal advice but as "attorney advertising" and you should always consult with a lawyer on any legal matter.
I assume you mean Suffolk County as it appears you reside in Hampton Bays. I also assume that the "divorce document" provides that the property, marital or separate, is to be transferred to you.
A deed requires a grantor and a grantee so whoever 9or whomever) is the property owner or owners need to sign a deed transferring it to you. But as stated above, there may be legal consequences to the transfer and I would suggest counsel.