The first five books are closely linked together - they are the "Torah" (Hebrew for "teaching" or "instruction") traditionally attributed to Moses. This explains why they can be called "The Five Books of Moses"; the Greek "Pentateuch" means "five books" and is another title for this section of the Bible.
Calling the books after Moses makes sense, and avoids some awkwardness with the more specific titles - Genesis and Exodus are good names, but Numbers really isn't, given that most of the book isn't about the census. Another reason is to stress the unity of these five books.
In Hebrew, the books are named after the first words in the text (the "incipit"):
- Bereshit - "In the beginning God created the heavens and the earth"
- Shemot - "These are the names of the sons of Israel who went to Egypt with Jacob"
- Vayikra - "And the LORD called to Moses"
- Bamidbar - "The LORD spoke to Moses in the tent of meeting in the desert of Sinai"
- Devarim - "These are the words Moses spoke to all Israel"
This is a common practice in many languages, for texts that don't come with their own titles. However, I don't think that languages other than Hebrew use these titles for the Bible books.
The standard names used in English derive from the Greek titles in the Septuagint. These are based on the content of each book:
- Genesis - How it all began
- Exodus - Leaving Egypt
- Leviticus - Concerning the Levitical priesthood
- Numbers - Starts with a census
- Deuteronomy - "Second law", or "a copy of the law"
I don't know why they did this as opposed to using the Greek incipits. That would have given us Arche ("the beginning") for Genesis, Onomata ("the names") for Exodus, and so on, matching the Hebrew. Nevertheless, these are the traditional titles that have come down to us, and which many translations have followed.
Most other Old Testament books have basically the same name in translation, since they tend to be named after people - Isaiah is Isaiah in any language. But there are differences too:
- Psalms is called Tehillim ("praises") in Hebrew; the Greek "Psalmoi" means "pieces of music"
- Ezra and Nehemiah used to be called 1 Ezra and 2 Ezra; even earlier, they were a single book of Ezra
- 1 and 2 Samuel, and 1 and 2 Kings are called 1 Basileion through 4 Basileion in the Septuagint. Hebrew formerly just had a single book of Samuel (Sh'muel) and a single book of Kings (M'lakhim).
- 1 and 2 Chronicles are called the Paraleipomena in the Septuagint, which means "supplementary"
In the New Testament, I think there is much more cross-language agreement about what to call the books. The only one that looks different is Revelation, which in many languages (including Greek) is called Apocalypse. But this means just the same thing as the English word "revelation" (and is "Offenbarung" in German, etc.).