The term 'Indian', initially applied to the indigenous inhabitants of the Americas when the 1492 expedition arrived in the area, is often misattributed to the alleged Columbus' belief that he arrived to India, but in reality this is a simplification of the term 'West Indian' derived from 'West Indies' - a distinctly different if not too creative name applied by the explorers to the islands in what is now called Gulf of Mexico (similar to 'Indies' that included India proper and all the lands that were not associated with China). Please note that in his journal, Columbus (or possibly Bartholome de las Casas who edited at least some of material later translations are based upon) uses the term 'these Indies' or 'discovery of these Indies', strongly suggesting that he was perfectly aware that the land he visited in 1492 was not the Indian subcontinent or any 'Indian' area known by contemporaries.

This name was further naturally applied to all native inhabitants to America and pretty much stuck in popular consciousness despite the development of the American polities and the contact with the local societies that were known under their indigenous names. Please note that the term 'West Indies' are still used today to informally refer to the islands located between Caribbean Sea and Atlantic Ocean, i.e. Antilles, Bahamas and Bermudas (it is not synonymous with the term 'Caribbean', as the latter typically also includes Eastern shores of Central America). The term has also been used in an official capacity, in the name of the West Indies Federation, a political entity that existed in the years 1958-1962, consisted of British colonies in the area and attempted to achieve joint independence. It has been dissolved after Jamaica and Trinidad and Tobago separately gained independence in 1962.

The differentiation between West Indies and East Indies (that included both Indian subcontinent, Southeast Asia and Malay Archipelago) is also reflected in the name of the colonial companies created in the beginning 17th century and operating in the area, namely English East India Company and Dutch Vereenigde Oostindische Compagnie (United East Indian Company).

Now, did Columbus know about America? According to our modern knowledge, he did not, much like anyone else. There is no evidence that anyone in Europe knew of the extent of the American landmass prior to the expedition in the end of 15th and early 16th century. For the reasons why Norse expeditions did not gain much renown, you might refer to this thread about the rumors of Vinland by u/y_sengaku and u/Platypuskeeper and this one concerning a similar topic with contributions from and u/y_sengaku and u/sagathain.

The main misconception concerning the 'discovery of America' is caused by the modern concept of 'America' itself. It is true that the earliest known historical mentions of the arrival of Europeans on the American landmass, further corroborated by the archaeological evidence refer to the Icelandic and Greenlandic expeditions led by Leif Eriksson, Thorfinn Karlsefni and other Norse explorers. They most likely arrived in the areas that are now known as Baffin's Island, Labrador and Newfoundland. But the area is not known to be explored further, possibly due to the adverse climatic conditions met by sailors and lack of pressure to colonize new lands.

The areas discovered by the Norsemen were known, at least by the scholars who had access to the appropriate literature, as they were described in e.g. Gesta Hammaburgensis ecclesiae pontificum written sometime in the 1070s by Adam of Bremen, or Cronica universalis, written in early 1340s by Galvano Flamma, a Milanese monk. An Italian historian, Paolo Chiesa, posited recently that Flamma might have received his information from contemporary sailors rather than older books, but there is little evidence to support this claim. But even if we include into our consideration the 'Vinland Map' that was first presented in 1957 and includes the areas similar to modern north Canada but is largely considered to be a modern forgery, it should be stressed that the 'America' was not a large, inhabited landmass spanning almost the entire distance between the north and south ice fields, but rather a 'cursorily explored island west of Greenland, possibly uninhabitable, because no one settled there for many centuries.' Thus, it can be said with very high certainty, that in 1492, no one in Europe fathomed that there might be an inhabited or even habitable land located on or near the equator and positioned between Africa and known Asia, looking westwards (the aforementioned document by Flamma also mentions only 'Markland', i.e. Eastern Labrador or Newfoundland). In other words, as of now, there is little evidence that the existence of the territory found by the Greenlanders in 10th century was a common knowledge. It could have been known to some scholars and navigators, but not many others. And it is almost certain that no one involved in the European maritime trade knew about any land further south of Newfoundland, so both the Columbus' surprise and the objections of the royal advisors who claimed that it was impossible and thus pointless to sail westwards from Europe to Asia were very much genuine.

Of course, all discussion about 'who discovered Americas', with Genovese, Spaniards, Norsemen, Chinese, Polynesians, French, Basques and Poles being usually mentioned as 'true' discoverers, is completely moot, as according to our best knowledge, the America has been discovered and colonized by East Siberian nations that came to Northern America crossing the natural bridge over what is now Bering Strait roughly around 20.000 BCE and later settled the entire continent. Anyone else is just 'another exogenous person who arrived to America' what is definitely less romantic than 'discoverer of America'. From historical standpoint, Columbus is renowned not because he was 'first', but because it was his expedition that set in motion a new era of European history that impacted the entire world.