Does the "no writing in the book" include a name written inside the cover of the book?  would it be ok to white it out and then post it?

From the Help Center:

No writing or highlighting or underlining on text pages

• a signature or note on the flyleaf or inside front or back cover is OKAY

So that would include a name written on the inside cover.  I would say just leave it.  It's fine by postablility standards, and the person who requests it might take more issue with the white out than just a name. 

I agree, just leave it -- I am always sort of annoyed when someone has cut a name out with scissors --  but I understand the privacy concerns for some people. If it is your name and you are concered about privacy, then do white it out buth otherwise, leave it. Edited to add: as others have said, White Out is probably the least desirable way to obliterate a name (other than cutting it out!)...scribbling it out or using a felt tip pen to obliterate it is probably best.

Its fine as is. I would strongly advise against using white out. White out is nasty and honestly, could be considered dirt on the book.

But, if you feel you must do something to it, it would be far preferable, IMO, to take a sharpie and just black it out.

A name inside the cover will not make the book unpostable.  And I agree, unless there's something unique (potentially unprivate) about the name, I'd just leave it alone.

I like a name or dedication in a book; it gives it some history.

I like a name or dedication in a book; it gives it some history.

I agree, just leave it alone. It does not make the book unpostable, and by whiting it out, someone might actually consider that ruining the book vs. just leaving the name there.