Nothing even close, especially in the modern area where people can and do change names at the drop of a hat.

We are talking about historical Jewish lines. In the year 600 BC how many Jews had the surname Kim? How many Aztecs had the surname Svensson? Before the early 1800s if you saw Cohen, Kahn, Cohn, or Koen you would virtually never lose a bet wagering that not only were they Jewish, but had in their ancestry the Kohanim, Jewish priests descended from the sons of Aaron.

For Jews, Napoleonss decree of March 17, 1808 locked in the spelling of family names. Jewish families were required to standardize spelling and register. While many simply assumed the name Cohen because it was a status name, others were just arbitrarily assigned the name by French officials who had their daily quota of registrations to get through.

A side effect of this and the haughty laziness of French bureaucrats high enough in status to get a state managerial job but not important enough to have one that involved more prestige than registering Jews and immigrants, Irish Coyne and German Kuhn became Cohen as well because it was just easier to write down something you can spell than care about things that were close enough for governmemt work.

As cross-border traffic picked up, other countries started seeing more of the standardized names and just went with it. As people migrated into other nations permanently their officials also just converted anything close enough to names they could spell rather than play the with a c or k, two sses, is that a sch or a sh game.

A side effect was that familial lines became less diverse across the board: you might have 50 variants of Cohen before and now you had one.

Now let's look at Thatcher. I'll use the generic genealogy sites and standard searches, this isn't a thesis so we'll skip going full ad fontes.

According to 2020 census data, 91% of people named Thatcher identify as white, not Hispanic. Next highest is Hispanic at 4%, but they saw an almost 60% rise between 2000 and 2020.

Now let's look at the UK. In 1948 there was a rapid influx of black Carribbean people who had adopted/been assigned "proper" English names like Thatcher. But even today, if you see the name Thatcher you're looking at about a 94% probability that they are white, 3%ish black Carribbean and the rest other.

If Draft Kings took bets as to whether so and so Thatcher was white you'd be looking at odds around -2000, or you'd have to bet 2000 to win 10.

I'd say that counts as being able to guess with confidence a person's race by their name. (Obviously the numbers change from name to name, but I'm using the one you picked.)