It's possible for vertebrae in the neck (or back) to be broken by an impact, but not actually damage or sever the spinal cord until subsequent movement drags the sharp edges over the sensitive nerve bundle.

This happens periodically in car accidents, which is why, after a serious collision, it's very important to stay put and wait for paramedics to get you out even if you feel like you can move everything. (Unless your car is on fire, in which case you might as well take your chances.)

There ought to be telltale marks in the sand--indentations, trails, that sort of thing from the victim's arms and legs--that would give you an indication of whether the victim's hand actually wrote the name, and if so, whether that hand was helped by someone nearby at the time. Anything that wipes away those traces will also wipe away the name.