It's not exactly a hideous name, but it does sound quite odd. This name just seems quite pretentious and old-fashioned, and I can't say I've ever heard of anyone named Sacheverell. I'm pretty sure most people couldn't pronounce it or spell it.
Reminds me of those eccentric old men who present Antiques Roadshow, making all those poor people who queue up, clutching what they think is a hidden gem from their attic, but all Sacheverell wants to do is talk bollocks while he adjusts his glasses further down his nose. I can hear it already: "Well it's an early 18th century piiiiiece. Has it been in your family looooong?" Who would want to call their kid a name that gives that kind of impression? Who can even pronounce it?! They'd end up calling him Shrapnel.
For anyone stuck with this odd name, Chevy could make a decent nickname. That is, if they don't mind Chevy Chase. He pronounces it 'chevee' though, whereas here it would be something like 'shevee'.
I first heard this in a Mr. Mulliner short story by P. G. Wodehouse. It's hard to imagine on an actual person, but it certainly is interesting. I like goricar's nickname suggestion.