Yes, it is called Judaism. Jesus was a believing Jew for his entire life and ministry. He criticized certain practices and interpretations of certain religious leaders of his day, but Jesus never abrogated or advocated any abandonment of the holy scriptures, faith in God, or living in accordance with the essential moral teachings or code one finds given us in those scriptures. Indeed, a reasonable interpretation of his ministry is that he sought to emphasize the essential moral character of the laws or rules, coming as he said to ‘fulfill’ or explain them in a more essential or complete fashion, rather than to overturn or invalidate any of them.
And while Christianity eventually came to have its own identification, the common Judeoj-Christian faith tradition teaches the same moral standards and values from the same holy scriptures, which we believe derive from the same One God and Creator.
We don’t need to read the word “Christianity” in the Bible to read, and follow, the Bible’s central moral teachings.
(Indeed, it would be an unfair imposition to demand that a certain word, one that probably did not develop or become commonplace for some time after the end of the Biblical canon, somehow be found inside that body of writings.)
At any event, that’s how I sees it.
Since you asked.
Best regards, fhc
As for Jesus following Judaism, well, He was born a Jew, of course. But He did violate the laws at one time or another. For instance, healing the sick on the Sabbath.
For a more serious violation of Judaistist practice, He claimed to be the Son of God, and never denied it, when asked, or told, by men, demons, of Satan himself.
Matthew 26:62-64 King James Version (KJV)
62 And the high priest arose, and said unto him, Answerest thou nothing? what is it which these witness against thee?
63 But Jesus held his peace, And the high priest answered and said unto him, I adjure thee by the living God, that thou tell us whether thou be the Christ, the Son of God.
64 Jesus saith unto him, Thou hast said: nevertheless I say unto you, Hereafter shall ye see the Son of man sitting on the right hand of power, and coming in the clouds of heaven.
Christ didn’t say, “I came to finish explaining the Law”, he said, “I came to complete it.” Let’s be clear: moral living to the standard of perfection the Law requires is impossible, which is the very point of Christ’s sacrifice: a sinless life that covers all sin.
Matt Chandler’s book, The Explicit Gospel, is one of the best treatments of this I’ve ever read.