Most proper nouns will be transliterated (i.e., the word is expressed in the characters of the target language). For example, the names of cities: Jerusalem = יְרוּשָׁלַיִם and Corinth = Κόρινθος. Often the transliteration is not exact. Here, the Greek word for Corinth is Korinthos and the Hebrew word for Jerusalem is Yerushalayim. These differences often arise for historical reasons. When Jerusalem was transliterated into Latin, there was no Y letter available and so a J was used instead (which was pronounced like a Y). Over time, the pronunciation of the Latinized name changed to what it is today, and now it is so widely used that Bible translators stick with it rather than use a more precise transliteration.
Occasionally a proper noun will be translated if the meaning of the name is particularly important, or the name is highly descriptive. For example,
So Abraham called the name of that place, “The Lord will provide”; as it is said to this day, “On the mount of the Lord it shall be provided.” (Genesis 22:14)
But the King James translators used a transliteration instead:
And Abraham called the name of that place Jehovahjireh : as it is said [to] this day, In the mount of the LORD it shall be seen (Genesis 22:14 KJV)
Even with transliterated names, if the meaning is particularly important the translators will usually provide it in a footnote.