The name "Cartagena" stems from Latin "Carthago Nova", which was originally a Punic colony founded by Hasdrubal Barkas in 228 BC with the name of Qart-Hadast. When Publius Cornelius Scipio conquered the town in 209 BC, he named it "Carthago Nova", literally "New Carthage".

The name of town Carthage itself comes from Phoenician "Karti-ha-daasti", meaning "Newtown" (compare Latin Villanova, Greek Neapolis, Swedish Nystad or Russian Novgorod). So Carthago Nova means "New Newtown".

The current name is due to the linguistic changes during the centuries when Latin spoken in Hispania transformed into modern Spanish.

There is also a town Cartagena in Columbia. It has been named after Cartagena, Spain, and its official name is Cartagena de Indias. The meaning of the name is the same, though.

More Info: en.wikipedia.org