About 2000 years ago Jesus Christ died on a cross. A person who is a believer in Jesus Christ and his teachings is called Christian. My question is what were people called who followed the Messiah before Jesus Christ?
The Messiah is a well-known type within Judaism. Prior to the incarnation of Jesus Christ (when Jesus, who was God, became man), there was no Christianity.
The word "Messiah" in Greek is "Christos" from which we get the term "Christianity."
The word "Messiah" simply means "appointed," and within Jewish thought, the Messiah was appointed by God to make radical changes. For more on this, see the question: What is God's good news before Jesus's death and resurrection?
Theologically, Christians claim to be the heirs of the promise given to the Jews, through Abraham. The distinction between modern Judaism and Christianity is whether or not we believe that Jesus of Nazareth is the Messiah, aka, "the Christ." That we are have the same understanding of what is good and bad morals is the link.
What separates us is whether or not Jesus was God. If Jesus is God, then he can save us. If Jesus is not God, we can only be saved by being part of the covenant given through Abraham.
Indeed, even for the first Century, the only distinction between "Jews" and "Christians," was that Christians were this sect of Judaism that believed Jesus was the Messiah predicted in the Jewish Scriptures. Unlike what mainstream Judaism would have taught, however, this Messiah was not a Jewish-only savior.
As this group of Jews grew, (they were known as "The Way" at that time), non-Jews (Gentiles) were seen to be part of the group as well. Initially, the question was how Jews should accommodate these Gentiles (see Acts 15), but by the end of the first Century, the situation was reversed.
All of this is to say, people who followed the Messiah prior to Jesus' would have simply been called "Jews"
(Side note, Hebrew is an ethnic identity, Judaism is a religion that originated amongst the Hebrews)