I’m not quite sure why Chalke is often associated with Lesbos. The small island is off the coast of Rhodes, not Lesbos. It’s part of the Dodekanese Island group along with Astypalaia.
Although the tiny island was long overshadowed by next door Rhodes, it allied with Athens and was therefore given some autonomy, which evidently allowed them to mint their own bronze coins, which today are relatively rare.
Per Greek mythology, the titans were the original settlers, but given their huge size and the tiny island, they moved elsewhere. During the migrations of the 20th century, the entire population left.
Due to the Greek alphabet, the island can be spelled Chalke or Halki, which is more commonly used today. It’s believed that the name came from copper workshops, since Halkos is the Greek word for copper.