Question: What are the most common names in the Bible?
Response: I am happy to give you some approximations, but please keep in mind that this information is not based on a personal calculation of all the Biblical names. To get an actual count, one would have to purchase concordance type software and crunch the numbers, and, for reasons that may become obvious in the answering of this question, that is more difficult than it sounds at first, so that an exact count may not be possible.
First, I assume you mean personal names, not place names. The divine name (Lord, God) in Greek and Hebrew is the most commonly occurring name in terms of how many times the name occurs. In terms of human beings, Jesus (His humanity), David and Moses appear to be the most commonly occurring names - although for Moses, I am aware of only the ONE Moses and ONE David. In the English Bible, Jesus is always Jesus Christ, however His name in Hebrew is the same as Joshua, and this is reflected in the Greek transliteration as well (we differentiate this identical name when translating into English). The most commonly occurring name that is not only a person but his offspring as well is Israel (many more occurrences of this than Jesus, David or Moses). Now, if you mean which given names are used by more different people, Simon (possibly 10 persons with that name) John (possibly 9 persons with that name), Elkanah, (possibly 8 persons with that name), Mary (possibly 7 people with this name) and James (possibly 5 persons with that name) top the list to my knowledge (although Elkanah is not one you would guess, and it is possible that there are some other names like it out there that may outrank others on this list). Even this answer is problematic, however, in that we are not always sure about the historical details of all of the persons mentioned in scripture, especially in genealogical lists, as to whether they are "the same John as" for example. This is also true with some of the personalities mentioned in the gospels. So, while there is probably no hard and fast answer, the most straightforward answer I can give, if I have understood your question aright, is "Simon, Elkanah, John, Mary and James - probably". As far as I know, unless you can find a reference work that collects all the biblical names and organizes them statistically, it would be impossible to say for sure. If you are interested in pursuing the matter further, I would recommend checking the articles in a good Bible encyclopedia which might be found in your local library (Hastings and Anchor are particularly good). They may not have the precise info either, but they usually do provide interesting information and additional bibliography which you may find helpful as well.
P.S. A later reader notes: "I thought I would mention Zacharia and Azaria among the list of most common names in the Bible. I believe both are mentioned separately for around 30 different people."
You might also find the following links helpful:
The "New Name" Christians receive in eternity
What is the significance of biblical name changes?
Pagan Names versus Christian Names.
What does the Name "Christian" mean?
The Name "Jesus"
The Name "Christ"
The Names of Jesus Christ
Divine Names in the Bible
Names of Antichrist.
Names of the Devil.
Hope this is of some help,
Yours in Christ,