It is the name of several characters in Greek mythology. The main ones are Laodamia, wife and widow of Protesilaus the Prince of Thessaly, who died in the Trojan War. She was the daughter of Acasto and Astidamia. There was also Laodamia, a daughter of Bellerophon (who killed Chimera and tamed Pegasus). There were other women named Laodamia. Name of an asteroid 1011 and it was also named 1924 PK.