I have the impression that the names Columbus and Copernicus are not the forms actually used on a daily basis by those people, but rather Latin forms used to identify them in in scholarly or academic connection.
The vast majority of Copernicus's surviving works are in Latin, which in his lifetime was the language of academia in Europe. Latin was also the official language of the Roman Catholic Church and of Poland's royal court, and thus all of Copernicus's correspondence with the Church and with Polish leaders was in Latin… The surname Copernik, Koppernigk is recorded in Kraków from c. 1350, in various spellings… During his childhood, about 1480, the name of his father (and thus of the future astronomer) was recorded in Thorn as Niclas Koppernigk. At Kraków he signed himself, in Latin, Nicolaus Nicolai de Torunia (Nicolaus, son of Nicolaus, of Toruń). At Bologna, in 1496, he registered… as Dominus Nicolaus Kopperlingk de Thorn – IX grosseti. At Padua he signed himself "Nicolaus Copernik", later "Coppernicus". The astronomer thus Latinized his name to Coppernicus, generally with two "p"s (in 23 of 31 documents studied), but later in life he used a single "p". On the title page of De revolutionibus, Rheticus published the name (in the genitive, or possessive, case) as "Nicolai Copernici".
The name Christopher Columbus is the Anglicisation of the Latin Christophorus Columbus. His name in Ligurian is Cristòffa Cónbo, in Italian Cristoforo Colombo and in Spanish Cristóbal Colón… Columbus never wrote in his native language, which is presumed to have been a Genoese variety of Ligurian…
How, when and why did Latin cease to be the language of international scholarly communication?