At the top of Form 4797, there is a section for "Identifying number", but I was unable to find anything in the documentation about it.
Is this just my SSN, or is it some other identifying number? Is this documented somewhere in the instructions?
I believe so. Looking at my own return, other forms specifically ask for social security numbers in that box which is (to the best of my knowledge) only used to help associate loose forms with your return if/when they are separated.
Other forms have (at least in the past) also said something like "SSN or taxpayer identification number" for the corresponding box.