Am I correct in thinking that a disproportionately large number of African-Americans have the surnames of early presidents?

If so, were slaves given their names by their owners or did they adopt these names on emancipation?

It’s a mix. Many took the names of their former owners. Others took “American” names. It’s not like there was an organization that officially assigned names.

Booker T. Washington wrote in his autobiography ("Up From Slavery” was one of the first 100 “Pocket Books”, together with “Lost Horizon” and “The Werewolf of Paris") that he chose “Washington” as an archetypically American surname, and that the “T.” stood for nothing but itself - he added it for the pure pleasure of being able to.

I seem to remember that there was a footnote in my copy of “Tom Sawyer”, to the effect that if Harding (whatever!) owned a bulldog called “Booker”, the dog would be referred to as “Booker Harding”, but if he owned a slave called “Booker”, the slave would be referred to as “Harding’s Booker”. But my memory could be at fault (sighs)

Totally off-topic, but George Washington seems to have impressed the Scots sufficiently. that quite a few were named after him in the 19th C. Notably, George Washington Wilson, a photographer who recorded a lot of Scottish daily life, and George Washington Sprott, church minister and theologian (both born in the 1820s).