Panama City gave its name to the country and, as explained in detail in my post
David is named after the biblical King David.
La Chorrera has always been thought to refer to the large number of waterfalls, although the name does not mean waterfall and does not translate at all.
Santiago de Veraguas has a Spanish prefix, meaning Saint James, and the name of the province, itself from an indigenous language where Veracua or Viragua was probably a proper name, although there are many (unproven) theories.
Penonome comes from peno Nome, where Nome was the local chieftain put to death by Spanish conquistadores when he dared to resist their rule. Peno Nome literally means 'Nome was punished'. Legend speaks of his love for a local woman named Zarati. However, the tribe didn't approve of their love and told him she had drowned. He is said to have thrown himself into the same river and perished, thus giving names to the Zarati River and a slightly different meaning for the place name of 'Nome mourned'.
Puerto Armuelles was named to honour Colonel Tomas Armuelles, a hero of the Coto War between Panama and Costa Rica and fought over a period of thirteen days in February and March 1921. Port Armuelles was named shortly after his death in a train accident on 18 March 1921, it had previously been known as Rabo de Puerco or 'pigtail'.
Chitre takes its name from the local tribe, the Chitra.
Almirante is the Spanish word for 'admiral'.
Last Tablas takes its name, according to folklore, from planks of wood salvaged from a Spanish ship which ran aground after fleeing from the pirate Sir Henry Morgan. The only evidence to support this is the literal translation of las tablas as 'the boards'.
Note the spellings of the places are English as the piece is written in English.