But
Jefferson is recognisable as a common patrynomic surname. So it fits in with modern surname as first name and -son ending trends. It can also serve as a more unique and less dated variant or way to honour
Jeffery. (That being said if you name your son
Jefferson I am going to assume you're a white supremacist until proven otherwise).
Whereas
Washington is pretty much inseparable from the president. It's not a common surname except among African-Americans whose newly-emancipated ancestors chose it in honour of
George. The only reason it ever got semi-regularly used as a given name was because of the US's ridiculous founding mythology, which thankfully most people see through now.
Also what do you think makes a better nickname or element:
Jeff or "Wash"? 😄 While Wash/Washing might not be the worst common noun to be named, to me at least the association is pretty strong and weird to think of as a name (although tbf I'm sure there are now many little Drydens running around).