Is there any paperwork out there that you have to get to sign any of your organs to someone specifically?

Need an attorney...: Typically organ donation can be done with a simple form; I do not know the legality of willing an organ to a specific individual; i'm sure there is a procedure involved but best to consult an attorney to carve out(no pun intended) the fine print of it.

Within UNOS system: Since bias would be ethically unfair, the system tries to prevent selection of who your organs can go to. Thus, "blue" donors are not allowed to select only "blue" recipients, or prefer "purple" recipient ahead of the "flowered" recipient who just made the appeal on tv. However, if you know someone already on the unos list, you (or family) are permitted to make a directed donation on consent form.

Not formal paperwork: I suppose you could write this in your will. Directed donations can and do occur after death. If you so desire you should make this clear to your direct family members who would have to make the request at the time of your death.