If Jehovah were an exclusive name for God the Father, then it would be appropriate for Jesus to have used that name, along with a myriad of other names (Jehova-Jireh, El Shaddai, etc.).
However, if the name "Jehovah" applied to the Trinity, then it would seem odd for Jesus to refer to the Father with a term that also referred to Himself as part of the Trinity.
Jesus most often uses "Father" when addressing the Father, which is a relational term.
At that time Jesus declared, “I thank you, Father, Lord of heaven and earth, that you have hidden these things from the wise and understanding and revealed them to little children; yes, Father, for such was your gracious will. Matthew 11:25-26 ESV
And going a little farther he fell on his face and prayed, saying, “My Father, if it be possible, let this cup pass from me; nevertheless, not as I will, but as you will.” Matthew 26:39 ESV
Then Jesus, calling out with a loud voice, said, “Father, into your hands I commit my spirit!” And having said this he breathed his last. Luke 23:46 ESV
When Jesus had spoken these words, he lifted up his eyes to heaven, and said, “Father, the hour has come; glorify your Son that the Son may glorify you. John 17:1 ESV
And now, Father, glorify me in your own presence with the glory that I had with you before the world existed. John 17:5 ESV
And I am no longer in the world, but they are in the world, and I am coming to you. Holy Father, keep them in your name, which you have given me, that they may be one, even as we are one. John 17:11 ESV
Father, I desire that they also, whom you have given me, may be with me where I am, to see my glory that you have given me because you loved me before the foundation of the world. John 17:24 ESV
O righteous Father, even though the world does not know you, I know you, and these know that you have sent me. John 17:25 ESV