Don’t we read Plato’s writings of what Socrates said?
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
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)
(also worth mentioning the Cratylus in this discussion; etymology was definitely something these people thought about)
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.