Actually, one of the rules is:

You will not die if you write your name here, but it is not recommended. (Arrow pointed at the cover.)

and also:

You can write with any pen: the color doesn’t matter. If you use a sticker with a name printed on it, there will be no effect. Please write directly onto the notebook. It would be a good idea to change your handwriting as much as possible.

But if that’s true then it implies you will die if you write it anywhere else, which breaks another rule:

When the (loaned) owner dies, the Shinigami writes their name in the book (This is not a numbered rule but something Ryuk states, which could be false).

Which can also conflict with Rule IX for an immortality hack:

The Death Note will not ever affect a victim whose name has been misspelled four times. IX

But then they already patched it I guess:

If a Death Note owner accidentally misspells a person’s name four times, that person will be free from being killed by the Death Note. However, if the Death Note owner intentionally misspells the name four times, the owner will die. XXXV
The Japanese version also includes:
The person whose name was misspelled four times on purpose will not be free of death by a Death Note.