Good question! 

I think a few new titles for HHB could be...

• The Horse and his quest (a play on the original title) 
• The Boy, the Horse, and The North (trying to keep it a classic LWW title) 
• The Prince's journey ( a bit of a spoiler, but works because you don't' know who the prince is) 

-KingEdTheJust

The thing is, the previous topics on the titles for Prince Caspian and the Silver Chair were both based on the premise that there is something inherently unsatisfying with the present title's form and construction - and thus presented that as the problem to be solved with a new title suggestion.

'The Horse and His Boy' by contrast is, for me at least, an incredibly inventive, witty, and intriguing title - the form alone, switching the nature of animal ownership on its head, is just beautifully clever in my opinion.

Could you therefore establish what it is you feel is lacking with the present title of The Horse and His Boy, such that we might be able to offer you better suggestions to address the problem at hand?

Posted by: @icarus

Could you therefore establish what it is you feel is lacking with the present title of The Horse and His Boy, such that we might be able to offer you better suggestions to address the problem at hand?

Oh, nothing against the title, but it may not satisfy every reader. Some might feel that a horse owning a boy may a little too obvious. Then of course there's that line Bree says, "If there had been any stealing, you might as well say I stole him." 

So the title may not satisfy every reader.

Posted by: @jasmine_tarkheena

Oh, nothing against the title, but it may not satisfy every reader.

Well... you could say that about any title of any book, really!  

Some might feel that a horse owning a boy may a little too obvious.

I would have thought, as @icarus said, that the whole point of the title The Horse and His Boy is that it's the opposite of obvious — it takes the obvious concept ("the boy and his horse") and turns that on its head completely. I remember being impressed with how original and witty that title was when I first encountered it as a 7-year-old!

The one drawback I can think of to the actual title is that calling it The Horse and His Boy could suggest that the horse is the central character and the story is told from his point of view, whereas in fact Shasta is much more the central / POV character than Bree (or anyone else, other than Aravis for the section of the story when she's with Lasaraleen in Tashbaan). But that's a really minor consideration. I can't think of any other possible titles for it that I'd like better. But it's fun to think what else it and the other Chronicles could have been called.