Saxby - Our Name
The Saxby name is not that common, but, equally, not highly unusual.
There's a Bert Saxby in the James Bond film, Diamonds Are Forever and there are numerous Saxbys if you scan the internet.
Some notables are Sir Robin Saxby (bigwig in the development of Microprocessors), Saxby Pies, Mark Saxby (musician in some folk rock outfit called Arnold) and Kerry Saxby-Juna (Australian athlete of some note).
Google will find you many more, including some American politician whose FIRST name is Saxby (go figure...)
This website shows the name is about the 3319th most popular name in Britain, although there seem to be more of us, relatively, than before.
The following maps show the distribution of people with the Saxby surname throughout the UK in 1881 and 1998
My father was the only boy in his family, as am I, so the name lives on through us (all my dad's sisters married and, unlike the case sometimes today, none kept their maiden name), although there are quite a few 'Saxbys' from our family out their with different surnames.
This website suggests the name probably originates from a placename, with Lincolnshire being the likely location. There are Saxby towns in England still, whilst the "Quick to draw sword" (short tempered?) origin is also mentioned there.
The Saxby, Leicestershire website.
Another couple of suggestions I've heard are that it may be Saxon or Norman in origin, relating to the person who looked after Horse.