David in Walters body

Actually, the book very vaguely describes that it is not Walter, but David.  This only becomes obvious right at the end of the novel.  The novel doesn't spell it out that David switched places with Walter like in the movie.  We can only think it's David after the following paragraph in the book...

p.344 (2nd to last page of the whole novel):

David says to Mother, "Use security hailing code David 31822-B.  And in the meantime, I'd like some music.  Richard Wagner.  Das Rheingold, act two.  The entry of the gods into Valhalla."

p.345 (the last words of the novel):

Turning, he walked out into the holding room, gazing contently down at row upon row of sleeping colonists.  His colonists.  His subjects.  He smiled.  His future.

Walter wasn't listening to music on the Covenant at the beginning of the book and, from the movie and novel, we know that David likes music.  Plus, the music selection just seems like David's style.  The last sentences in the book almost spell it out that it is David and not Walter.  Using the David code could almost spell out that it is actually David too.  Thankfully I watched the movie first, so it was easy to think through the ending of the novel and actually know that it is David and not Walter.

So, there is no inclination that David switched chips or bodies with Walter in the novel.  That theory can only be deducted from the movie and not the novel.

David didn't swap programming with Walter. It's David in his own body we see on the ship at the end, he's wearing Walter's clothes pretending to be Walter. David cutting his hair early on foreshadows this. Walter is still on the planet, presumably shut down or disabled in some way. If it was a simple programming thing then David and Walter would not have to look alike for it to work. 

Ridley Scott explains the switch in this Podcast: Alien: Covenant Spoiler Special With Sir Ridley Scott

I think that it could be David in Walters Body as he would in essence still be David just a different body,  but we have to ask how would he had done this?

The other option would be David swapping clothes etc, and this is what i was lead to more, and RS had as Svanya mentioned... he did confirm that David had stole his clothing and cut himself and his hand off to appear like Walter.

Thanks for replying and the info guys,that fight was so fast and finished is a strange way still a cracking movie don't care what people/critics say about it. bring on the next one 

David wouldn't mind that - silly joke

 W alter (Weyland Alterego) said at  David "I cant leave you here.." so Walter is hosting David.. dont play with bullshit as David can cut his hand (was eated by a neomorph non cutted goddmn)and change hair and dress in 60 seconds 

Dreams will be the key of this fight in to a twin cybernetic 's personality

I really hope David is within Walter's body as the opposite creates very unnecessary questions like: 

why did david make a scar on his face when nobody had seen the scar on walter?

and

how did he have enough time to scar himself, remove his hand, and change clothes?

I really hope RS is just trying to misinform the audience, as this idea really complements the "evolution of AI" theme they are moving towards and its something i find very interesting. Bonus points to RS if he decides that Walter voluntarily allowed David to body swap/integrate into his programming. 

(i say that with a tinge of apprehension as i really loved Walter and, at first, i had wanted Walter to show up at Origae-6 with the engineers and save the day. But if Walter was convinced to join David, it would be a much more interesting twist and also further the "AI taking over" thing.)