First, here are the times when he appears in the Bible by name.
While I, Daniel, sought the meaning of the vision I had seen, one who looked like a man stood before me, and on the Ulai I heard a human voice that cried out, “Gabriel, explain the vision to this man.” When he came near where I was standing, I fell prostrate in terror. But he said to me, “Understand, O son of man, that the vision refers to the end time.”
I was still praying to the Lord, my God, confessing my sin and the sin of my people Israel, presenting my petition concerning the holy mountain of my God—I was still praying, when the man, Gabriel, whom I had seen in vision before, came to me in flight at the time of the evening offering. He instructed me in these words: “Daniel, I have now come to give you understanding.”
Then Zechariah said to the angel, “How shall I know this? For I am an old man, and my wife is advanced in years.” And the angel said to him in reply, “I am Gabriel, who stand before God. I was sent to speak to you and to announce to you this good news. But now you will be speechless and unable to talk until the day these things take place, because you did not believe my words, which will be fulfilled at their proper time.”
In the sixth month, the angel Gabriel was sent from God to a town of Galilee called Nazareth, to a virgin betrothed to a man named Joseph, of the house of David, and the virgin’s name was Mary.
These are the times when Gabriel is mentioned by name. According to the Catholic Encyclopedia, “it is not unreasonable to suppose with Christian tradition that it is he who appeared to St. Joseph and to the shepherds, and also that it was he who ‘strengthened’ Our Lord in the garden.”
These last appearances are not confirmed by the Bible, but are beliefs handed down over the centuries by various saints.