Did enslaved persons take their owner's surnames?

This is outside my area of expertise, so I am basing this answer on information from Elizabeth Regosin, Freedom's Promise: Ex-Slave Families and Citizenship in the Age of Emancipation. University Press of Virginia 2002.

In Chapter 2, "We All Have Two Names" Surnames and Familial Identity, pp. 54-78, Regosin lays out a complex situation regarding surnames of formerly enslaved people. She appears to have based her research primarily on pension records of Civil War participants, in particular the depositions of pension claimants.

Most enslaved people did not have surnames, and after being freed some had to pick one on the spot, e.g. when joining the military. Such a name was sometimes not even known to other family members. Choosing the surname of a former owner appears to have been a common, though far from universal, practice:

p. 68:

Despite historians' tendency to point toward the opposite, many former slaves assumed the surname of their last master.

p. 59:

Some freed people took the name of an original owner or an owner from their distant past to recognize ties to family members also owned by them.

One aspect making the derivation of surnames less than obvious at times is that most of the formerly enslaved people were illiterate and therefore knew the surname they used only in oral form, which then led to diverse spellings being recorded. Regosin explores one such case in detail, where after a lengthy process

p. 62:

Lucinda Twine received the pension for her son, the soldier "Anderson Twine, alias Toyan."

TL;DR is that it looks like that's true.

There's an open question about this issue specifically relating to New York on our Genealogy sister site. However, the only answer there (from a moderator, fwiw) just includes resources for how one might go about figuring that out themselves.

I know anecdotally I've always heard the tendency was to have the surname of a slaveowner somewhere up the line, or alternatively a "free" name of their own devising, often taken from our more famous former presidents (Washington, Jefferson, etc.)

I don't like to traffic in anecdotes though, so let's try something slightly more scientific (although not quite there I'm afraid), but amenable to historical research: We'll go through a list of famous former slaves and see where they got their surnames.

Before I really dive into the details, a trigger warning (for people other than the asker): I'll try not to be crude, but any discussion about this topic is necessarily a discussion about slavery and rape. If you have personal trauma related to these subjects, there's a nice question about the Zamboni you might be interested in. If it merely makes you uncomfortable, well it damn well should.

• Sally Hemmings - Surname of her first white ancestor: her grandfather, the captain of the slave ship her grandmother was brought over on.
• Absalom Jones - Picked it himself because it sounded "more American" than his Dutch former slaveowner's surname.
• Alfred Blackburn - Surname of the owner at his last plantation.
• Alfred Francis Russell - The surname of his rumored white father.
• Amanda America Dickenson - The surname of her white father.
• Amos Fortune - Given the surname by his slaveowner.
• Anna J. Cooper (nee Haywood) - Took the surname of her white husband after freedom. Before that, had the surname of her white father.
• Archer Alexander - The surname of his enslaver when he was born.
• Archibald Grimké - The surname of his white father/enslaver.
• Augustus Tolton - The surname of his enslaved father (not sure where his father got it)
• Bass Reeves - The surname of his enslaver.
• Henry Bibb - The surname of his white father (a Kentucky Senator).
• Booker T. Washington - The (first) name of his stepfather when the family was freed and he was first asked for a surname. The "T." he picked up later, when he found out his father was likely a member of the prominent (white) Taliaferro family.
• Clara Brown - The surname of her last enslaver.
• Cudjo Lewis - Possibly an Anglicization of his patronymic when he was taken as a slave in Ghana.
• David Drake - The surname of his first enslaver.
• Denmark Vesey - The surname of his enslaver.
• Dolly Johnson - The surname of her last enslaver (and likely father of her children), President Andrew Johnson.

That gets us A-D on the list (plus Hemmings, because I was interested. Her mother would have been on this list anyway.). I'm not sure I'm up to the work of doing the whole list, but perhaps its a somewhat representative survey.

Things I'm noticing:

• There are some exceptions, but the vast majority of the names, (14 of 18 on this list, or 78%) came from the surname of an enslaver.
• An (appallingly) large % of those enslaver surnames (50% on this list) were a paternal ancestor of the person in question. This kind of takes that behavior past the realm of "common" and well into "routine".
• Of the 2 presidential surnames on the list, one came from a first name of a parent, and the other from the actual president in question.

So, yes it looks to me like that is true. It seems most surnames came from an enslaver of the freed person. Perhaps somewhere in the vicinity of half were additionally the surname of a white paternal ancestor.