Can anyone tell me why/how Capitol came into being as the name for U.S. legislatures?

Capitol...from the latin Capitolium(from caputhead?) Any building housing the U.S. Congress or a state legislature, in this case also called Statehouse.

Yes, captiolium, from the name of one of Rome's seven hills, and home to the temple of Jupitor, is the root to capitol, as in "our nations Capitol"-- and the legislative body there--"Capitol Hill".

a related root word capo– meaning head is at the head of many other words

kaput, capitate, (and decapite) capo, captain, caprice, cape, cap– some have come in through a backdoor– kaput comes in from the german– (headless) or dead. "capitate" to head something-- lead to capital as an Upper case letter, and to money-- as capitol.. I can't remember all the other words where the head is hiding -- but i am sure the list will grow.