Clark (and Clarke) comes from clerk—itself from Latin clericus. In medieval England a “clerk” was not only an office worker; the word covered scribes, secretaries, and educated men in or around the church, because literacy clustered there. Naming someone Clark marked a skill: reading and writing when most people did not.
The surname is occupational/status, not a place. Spelling bounced between Clark and Clarke without changing the meaning. Some Irish Cleary/O’Cleary lines were later written Clark in English contexts, which is a separate Gaelic story sharing letters. For most US Clarks, the plain English clerk/scribe sense is the right first explanation.