Did the Trinity as we know it, God the Father, God the Son (also known as the Word), and God the Holy Ghost exist before creation? In other words, was Jesus known as Jesus prior to his being born as a man?

Jesus is the earthly name of the Son of God. The angel spoke to Joseph concerning Mary, "And she shall bring forth a son, and thou shalt call his name JESUS: for he shall save his people from their sins" (Matthew 1:21And she shall bring forth a son, and thou shalt call his name JESUS: for he shall save his people from their sins.
See All...). He was not called Jesus before His birth because Jesus refers to His humanity.

Isaiah 9:6For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.
See All... begins, "For unto us a child is born, unto us a son is given." Notice that the son is given. That which is given already exists. As the Son of God, Christ existed into eternity past. He was rich but became poor so that we through His poverty might be rich (2 Corinthians 8:9For ye know the grace of our Lord Jesus Christ, that, though he was rich, yet for your sakes he became poor, that ye through his poverty might be rich.
See All...). But notice also in Isaiah 9:6For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.
See All... that the child was born. Birth indicates the beginning of something. The Word, the Son of God, had never been a child before He was given to this world and born as a baby in the manger in Bethlehem.

When Jesus was born, He did not subtract anything. He had always been God and was still fully God. However, He did add something. Now, we was also man. The Word, who was God and who created all things (John 1:1-3 [1] In the beginning was the Word, and the Word was with God, and the Word was God. [2] The same was in the beginning with God. [3] All things were made by him; and without him was not any thing made that was made.
See All...), "was made flesh, and dwelt among us" (John 1:14And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
See All...). He always has been and always will be God, but He became a man.