I have to correct some of the things in the previous answer and would like to thus more fully and accurately address your question.
The God of the Prophets
God often refers to Himself as the "God of Jacob," the "God of Isaac," "the God of Moses," and similar phrases.
Quran: "We shall worship your God, the God of your fathers, Abraham and Ishmael and Isaac..." Surah 2:133
Bible: "I am the God of your father, the God of Abraham, the God of Isaac, and the God of Jacob." Exodus 3:6
"I am the God of your fathers, the God of Abraham, Isaac and Jacob..." Acts 7:32
So, followers of a single prophet was in really a follower of the God that the prophet served, and it is better worded as such. As in, don't say "followers of Noah" or "followers of Moses," but say "followers of the God of Moses."
The Line of the Prophethood and Their Religion
There was originally only 1 "religion," the true religion that worshipped the one true God that exists. These people were, for the vast majority, primarily Jews (as in by culture and descent, not the followers "Judaism" of today). Jews are the descendants of Isaac, and the Jewish descent is the line of the prophethood, which means that all the accepted prophets should be in the line of Isaac.
Q 29:27 "We gave him Isaac and Jacob, and placed the Prophethood and the Book in his progeny - thus We gave him his reward in this life, and in the hereafter he will surely be among the righteous."
Genesis 21:12 "But God said to Abraham...for through Isaac shall your offspring be named."
Now to the complicated part. Three different religions, Islam, Christianity, and Judaism, all claim that the prophets were followers of their respective religion and their religion is the one true, original religion that all the prophets worshipped. The prophets were Jewish by culture and submissive to God. According to the Quran, the prophets were Islamic by religion. So, any followers/believers during the Old Testament times are said to be followers of Islam, or Muslims (multiple quotes in the Quran about the prophets saying they are Muslim, such as Surah 3:67). All Christians, Jews, Muslims, Mormons, etc. all believe they are submitting to the teachings of God, but not all are actually Muslim, so this is clearly an incomplete test for seeing if you (or the prophets) are Muslim are not. Nowadays, a Muslim must recite the Shahada, believing that Muhammad is Allah's prophet.
Followers of Jesus (the Christ) = Christians
When it comes to Isa:
- Jesus, His followers, and the early Christians were mostly Jews. That is, Jewish by culture, descending from Isaac and Jacob. Jesus was in the prophetic line of Isaac, and all his 12 disciples were Jews.
- Followers of Jesus were called Christians by the mid 1st century. By followers of Jesus, I mean His disciples, which referred to Him as "Son of God" (Matthew 14:33, 16:16), "Lord" (over 500 times in the New Testament, e.g. John 20:28, Romans 10:9, Philippians 2:10-11), and "God" (John 20:28 and 6 other times in the New Testament).
Acts 11:26 "The disciples were first called Christians at Antioch."
Acts 26:27-28 (Paul speaking) "King Agrippa, do you believe the prophets? I know you do.” Then Agrippa said to Paul, “Do you think that in such a short time you can persuade me to be a Christian?”
"Christian" was likely originally a derogatory name meaning "little Christ," indicating the Christian's desire to emulate Christ (whom is Jesus). Christ (contrary to the previous answer) is a word used to denote Jesus over several hundred times in the New Testament (around 500 times). Christ is the Greek translation of the Hebrew word Messiah, both of which mean "Annointed One." The phrase "Jesus Christ" is used over 100 times in the New Testament, indicating that Jesus (the person) is the Christ (the title of being the Messiah).
Josephus (37-100 AD), Jewish Historian, Antiquities of the Jews, Book 18, Chapter 3 "About this time there lived Jesus, a wise man. He won over many Jews and many of the Greeks...Pilate...had condemned him to be crucified...and the tribe of the Christians, so called after him, has still to this day not disappeared."
Tacitus (56-117 AD), Roman Historian and Senator, Annals 15.44 "Nero fastened the guilt ... on a class hated for their abominations, called Christians by the populace. Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilatus..."
Note: the previous answer mentioned that the Bible wasn't written until 300-600 years after the crucufixion, but this is quite factually incorrect. It was written in the same century, before the end of the 1st century AD, and most scholars agree on that. No scholars think it is beyond the 2nd century. See this link on a test for historical reliability of the Bible, The Bibliographical Test, but almost any simple google search can give you a more accurate number less than half that of the 300 years after suggested by CreativeDip. Such as the wikipedia on Historical Reliability of the Gospels.
Origin of Judaism
Short version: Modern Rabbinic Judaism began with the Council of Yavneh (Jamnia in English) in 90 AD, where they had to rewrite everything Jewish to account for the destruction of the sacrificial system since the temple was destroyed in 70 AD. This is confirmed by a Jewish Rabbi and semi-confirmed online (need more research); sources are difficult to find quickly due to many incorrect theories about the Old Testament canon at that council (see Council of Jamnia; see The Canon of Scripture for more on canonization). It is around this time that modern Judaism come up and separated from Christianity. Christianity would claim that Christianity "fulfills Judaism" because Jesus said that he "fulfilled the Law and the Prophets" Matthew 5:17. Followers of modern Judaism would claim that Christianity is an offshoot of Judaism that diverges from what the prophets taught. Here are a couple small resources: pdf, pdf.
Followers of the God of the prophets, are called Muslims according to the Quran and are also Jews because of their culture/geneology. Followers of Jesus are called Christians, and they would also say that the prophets are "Christians" in the sense that they understand Muhammad to be a message contrary to the prophets that came before and thus reject it. Jews that reject Jesus as Messiah and the Son of God are followers of Judaism. Same story applies with them.