Wikipedia lists 27 countries that are named after real people, and 14 that are named after mythological or legendary figures. Just one of the real people, and one of the legendary figures, are women.
The island nation of St. Lucia is named after Saint Lucia (Lucy) of Syracuse, who was martyred during what is known as the Diocletianic or Great Persecution – the last and most severe persecution of Christians in the Roman Empire, in the early 4th century AD. She is one of eight women along with the Blessed Virgin Mary who are commemorated by name in the Canon of the Mass (the part of the Roman Catholic Mass that begins after the Sanctus with the words Te igitur).
St. Lucia is one of the Windward Islands, lying to the south of Martinique and to the north of St. Vincent. It was shown, as El Falcon, by the Spanish navigator and cartographer Juan de la Cosa on his famous map of 1500, which was the first European map to show the Americas. In 1502, Christopher Columbus (on his fourth voyage) made landfall on Martinique, but he didn't mention St. Lucia. A globe in the Vatican, made in 1520, shows the island as Sancta Lucia.
According to legend, French sailors were shipwrecked on the island on 13 December, which is the feast day of St. Lucia. (We don't know what year this happened – it's a legend.)
The country that's named after a legendary or mythological woman is the Republic of Ireland, which is known in its own language as Éire. Ériu (or Éire in modern Irish) is described on Wikipedia as "the eponymous matron goddess of Ireland."
Wikipedia also lists 25 dependent territories that are named after people. Unless I'm mistaken, four of them are named after women: Norfolk Island (named by Captain Cook in 1774 after the Duchess of Norfolk, who unknown to him had died the previous year), the North Mariana Islands (named after Mariana of Austria, who was Queen of Spain along with her husband Philip VI from 1649 until his death in 1665), St. Helena (named after the mother of Constantine, the first Christian emperor of Rome) and the Virgin Islands (named after the Romano–British princess St. Ursula, who was massacred in AD 383 along with her 11,000 handmaidens).
© Haydn Thompson 2019