Sophist means teacher, wisdom [1],[2]

kratos means power, or ruling [3]

How big is the probability that somebody is named 'ruler of the wise' and then becomes arguably the most influential philosopher of all time?

[1] https://en.wikipedia.org/wiki/Sophist

[2] https://en.wikipedia.org/wiki/Hagia_Sophia

[3] https://en.wikipedia.org/wiki/Aristocracy_(class)#Etymology

The first part of the name "Socrates" (Σωκράτης) comes from "sos" (σῶς), meaning "whole," not from "sophos" (σοφός), meaning "wise."

You'll note that "Socrates" and "sophos" have different vowel sounds (omicron vs. omega), and that the accented syllable in "sophos" is missing from "Socrates."

The "-crates" suffix indeed derives from the word for "power," but it's common in ancient Greek names: Philocrates, Hippocrates, Crates of Thebes, etc.

Thanks for the correction.

Do we know for a fact it was a given name and not a nickname?

(also worth mentioning the Cratylus in this discussion; etymology was definitely something these people thought about)

People with suitable names often seem to be over-represented in a field.

Cute, but no one is really sure why.

So while his name seems a tad much, that in itself isn't enough to disprove he existed.

(This is even more true in cultures where names usually mean something - think Hebrew biblical names)