Caterina/Catarina is a stunning, classy name that is surprisingly rare. It seems like Katherine/Catherine has won the hearts of most parents, leaving this gem to be found by those looking for something beautiful and underused. Caterina was given to 43 girls in 2016, with data since at least 1904 (with 5 births that year). Catarina was given a bit more in 2016 with 60 births. Also, Catherina and Catharina were each given a mere 5 times in 2016. This name definitely falls into the "familiar but rare" category. Caterina is an Italian and Catalan variant of the Greek name Katherine, which is generally accepted to mean "pure," from the word katharos. However, that meaning was largely a Christian take-over of sorts, and it could just as easily be from hekateros, "each of the two," or, slightly less likely, from the goddess Hecate, meaning "far off."
For famous namesakes, there's Italian noblewoman Caterina Sforza, born in 1463. She was Countess of Forli, Lady of Imola, illegitimate daughter of the Duke of Milan. Not just a pretty face, she dabbled in alchemy, hunting and dancing. If you go a bit further back in time, Caterina Appiani, born 1398, was lady of Piombino, of the Appiani dynasty. Catherine Cornaro, known as Caterina in Italian, was the last ruler of the Kingdom of Cyprus.
Another strong woman was Caterina Segurana, who played an inspirational and fierce part in the siege of Nice in 1543, enabling her city to win the battle.
Then there's Saint Katherine, born Caterina de Vigri. Born in an upperclass Bolognese family, she was lady-in-waiting to Parisina d'Este, who was married to the Marquis of Ferrera. Caterina is the patron saint against temptation and of artists, and she herself was an artist, as well as writer, teacher and mystic. Caterina Assandra, born 1590, was a nun and composer from Pavia, Italy.
In literature, there was Caterina Grimani, a character in Cornelia Funke's The Thief Lord (one of my highly recommended books). There's also seven songs about or titled "Caterina."
For the spelling Catarina, nobles include the Portuguese Infantas Catherina of Braganza, Catarina the Duchess of Braganza, and Catarina of Portugal. There's also the ballet Catarina that is also called La Fille du Bandit, by Jules Perrot.
The variants Catherina and Catharina have their own namesakes as well, including Renaissance painter Catherina van Hemessen. Catharina, in fact, has too many to mention. Catherina has two notable royals.