Deb at Adventures in Genealogy has a useful post on resources for tracking the changes in our immigrant ancestors' given names. When going back, it is helpful to have some sense of what our ancestors' names might be translated to in their native languages or what the name might have become in the US. Because of common histories and religious traditions, many originally Hebrew, Greek or Latin names have been adapted to various local languages. Peter, Per, Pierre, Boutros, Pietro and Pedro can all trace back their name to the Greek pétros (Πέτρος) 'rock' from the Apostle Simon Peter. In many cases, our ancestors simply changed their name to the appropriate English version. However, in other cases, they might have kept the old name (like my great grandmother Suzanne), adopted a similar sounding name with a different origin (M*A*S*H's Jamie Farr's given name was Arabic Jameel "beautiful"), or chosen a name with little obvious similarity.
Wikipedia as a tool for discovering different versions of a name
One useful tool for discovering different versions of a given name is Wikipedia. Take the name Matthew. In English, find the Wikipedia page for St. Matthew. It is best to find the earliest bearers of the name. Now find the sidebar on the left and look for a list of languages. You will find a list of more than fifty languages. The language names are in their own language, so you might have to figure out what the native name for a language is. In some cases, it is easy to make an educated guess. In other cases, the names will be unrecognizable, such as Cymraeg for Welsh, Magyar for Hungarian or Suomi for Finnish. Now try a few. You can find that the French (Français) version is Matthieu, the Geman (Deutsch) version is Matthäus, the Czech (Česky) is Mattouš, the Lithuanian (Lietuvių) version is Matas, and the Breton (Brezhoneg) version is Mazhev.
Figuring out Matěj Jaros
You can also search the different language versions of Wikipedia if you have the name in another language and want to find out what the English version might be. For example, take the Czech name Matĕj. This is the first name of one of my wife's ancestors from Písek in what is now the Czech Republic. Matěj has always been somewhat of a challenge to track because he would often come up with different names in different records. He is listed as Michael in the 1900 Census and his wife's death certificate, Matt in the 1910 Census, Matthias on one of his son's birth certificates, Matej on his death certificate and tombstone. Once you have found the Czech Wikipedia for Matěj, find the sidebar and click on English. Here you will find that the English version of Matěj is Matthias, explaining at least one of the records.