Before dealing with the main subject, we must note that Jehovah is a flatly wrong English translation of the revealed divine Name. To support this statement, I must deal with two issues: the history of Tetragrammaton use by Post-Exilic Jews and the history of Hebrew writing.
Regarding the first issue, after ca. 300 BC Jews started to avoid pronouncing the Tetragrammaton, first restricting its use to priests in the daily liturgy, then, probably after the death of Simeon the Righteous ca. 200 BC, further restricting its use to only the High Priest in the yearly Yom Kippur liturgy, and finally, after the destruction of the Second Temple in 70 AD, ceasing to pronounce it all. Thus, when reading aloud a Scripture passage in a religious service, any occurrence of YHWH in the text was replaced by "Adonai" (Lord) or, if it was immediately preceded by "Adonai" in the text, by "Elohim" (God).
Regarding the second issue, Hebrew writing was originally purely consonantal, so that the context of a word indicated its vocalization. Starting in the 6th century AD, the Masoretes added diacritical signs (niqqud) to the consonantal text to denote vowels. But in a few cases, the vowels denoted by the niqqud are not those of the word written in the text (the ketiv = "[what is] written") but those of the word to be read in its place (the qere = "[what is] read") . The Tetragrammaton is one of those cases, so that the vowels added to YWHW are those of "Adonai" (in most cases) or of "Elohim".
Now, if someone who ignores all this reads a Hebrew Bible, he may think that the vowels added to YHWH are those that pertain to it, and conclude that the divine Name is Jehovah. But that conclusion would be flatly wrong.
Having cleared this preliminary issue, we can now ask "Why don't Christians address God by the Name YHWH (whatever its right vocals are)?" The obvious answer to this question is "Because Jesus never addressed God by the Name YWHW", which in turn leads to the question "Why did Jesus never address God by the Name YHWH?", which has already been asked and answered in this site, including by me . For the sake of completeness, I will give a somewhat reworked version of that answer below.
First of all, let us recall two statements at the beginning and end of Jesus' High Priestly Prayer which make it clear that, for Jesus, making known to us the Name of God was a matter of prime importance:
"I revealed your Name to the men whom You have given Me out of the
world." (Jn 17:6)
"And I made known to them your Name, and will make it known, so
that the Love with which You loved Me may be in them, and I in them."
Since Jesus referred to God as his Father or "the Father", and the Apostles in their Epistles referred to God as "God the Father" or, in longer words, as "God, the Father of our Lord Jesus Christ", if we assume that the Apostles received correctly Jesus' revelation of God's Name, then "God the Father", understood as "God the Father of a consubstantial Son", is the fullness of the Name YHWH, just as Jesus' New Law is the fullness of Mosaic Law.
But now we may ask: in what sense is the Name "God the Father" the fullness of the Name YHWH? To answer that, we must recall that two divine Names were revealed to Moses in the burning bush, a Name in the first person, "Ehyeh" = "I Am", in Ex 3:14 (which Jesus applied to Himself in Jn 8:24,28,58 and Jn 13:19) and a Name in the third person, "YHWH", in Ex 3:15.
Now, whereas the Masoretic text provides the vowels of the first Name, so that its meaning of qal (simple) stem, first person, singular, imperfect form, of the verb "hyh" = "to be", i.e. "I Am", is unequivocal, it does not provide the vowels of the second Name, so that in principle it can be either the qal stem "Yihweh" = "He Is" or the hifil (causative) stem "Yahweh" = "He causes to be"  . The second option is supported by three facts:
a. Teophoric names of people (e.g. Netanyahu) and places, plus the shorter form of the name, Yah, have "a" and not "i".
b. The causative meaning implies the qal, since only Subsistent, Absolute Being can cause contingent beings to be, i.e. create them and sustain them in existence.
c. While the first Name expresses Who each divine Person Is  in Himself, Subsistent, Absolute Being (as Unbegotten, Begotten and Spirated respectively), the second Name in the causative meaning expresses Who each divine Person, and the three Persons altogether as one efficient cause, is for creatures: the Creator and Sustainer, He Who causes creatures to be.
Now, since creating, causing creatures to be, is not something that God did by necessity of nature but something that He freely decided to do, the Name Yahweh, in contrast to Ehyeh, does not express Who God Is in Himself but only from the viewpoint of creatures. (For whom that sense of the Name in the third person is essential, because if God had not created there would be no creature to pronounce his Name in the third person. So for God's Name in the third person to be pronounced, God must create and therefore be, from the viewpoint of creatures, "He causes to be".)
Bringing now into play Jesus' revelation that God as First , the First divine Person, begets/generates eternally a consubstantial Son and therefore is "God the Father", we can immediately perceive this parallel:
YHWH = He causes (contingent creatures) to be (contingent sense), by an act of free will.
Father = He generates (one consubstantial Son) to Be (subsistent sense), by nature.
whereby we can immediately understand that the Name "God the Father" is an infinitely fuller version of the Name Yahweh, as the generation of a consubstantial Son, Who Is all that God the Father Is (except Father), is an infinitely higher act than the creation of contingent creatures, each of which participates in a limited, finite way the divine fullness of Being.
To note, we do not say that God the Father "causes his consubstantial Son to Be" (whereby the parallelism would be even greater) because the "narrow" sense of the Latin word "causa" denotes difference of substance between cause and effect, but we could even say that if we used "cause" in the "broad" sense of the Greek word "aitia", which can also stand, and in this case would stand, for the sense of the Latin word "principium", denoting numerical sameness of substance between begetter/generator and begotten/generated .
Importantly, both divine Names have their respective professions of faith in Scripture. For the Name YHWH, it is the Shema in Deut 6:4:
"YHWH Eloheinu, YHWH Echad." = "YHWH our God, YHWH is One."
For the Name God the Father, which implies God the Son, it is the profession of faith in 1 Cor 8:6, whose parallelism with the Shema becomes more evident if we italicize the (reasonably added) words that are not in the Greek text , as I did below:
"to us there is one God the Father, of Whom are all things, and we
for Him; and one Lord, Jesus Christ, by Whom are all things, and we
Thus, Jesus, by revealing Himself as "I Am" (Jn 8:24,28,58; Jn 13:19), one with the Father (Jn 10:30), simultaneously reveals that God is not only "He causes (limited creatures) to be" contingently ad extra, but first and foremost "He generates (a consubstantial Son)" esentially ad intra. God as First, the First Person, is by nature both "I Am" and "Father", the begetter of a consubstantial Son. Thus, "Father" from the viewpoint of Jesus, and "God the Father" from our viewpoint, is an infinitely fuller version of the Name Yahweh.
In addition, just as the Name Yahweh presupposes the Name Ehyeh, "I Am", because no contingent being but only the Subsistent, Absolute Being can cause contingent beings to be, i.e. create them and sustain them in existence, the Name God the Father, understood in the orthodox sense of "God the Father of a consubstantial Son", presupposes the Name "I Am", because no contingent subject but only the Subsistent Being as First, the First Subsistent Hypostasis, can beget a consubstantial Son, i.e. a Son who is numerically the same substance (understood in a particular, not a universal sense) as the Begetter.
Finally, in addition to revealing Who God Is in Himself, the Father that by nature generates eternally a consubstantial Son, Jesus has revealed that God the Father has decreed to make us his adoptive sons, not just in name but in fact (1 Jn 3:1), by making us partakers of his consubstantial Son (Heb 3:14) by grace, i.e. by transforming us in the image of, and uniting us to, his Son. Thus, Jesus has revealed that God is, for us, not only YHWH, "He causes (us) to be (creatures)" by creating our nature, but also "Abba", "Father", "He causes (us) to be his adoptive sons in his only consubstantial Son" by infusing us with his grace. Since what God causes us to be by his grace, i.e. his adoptive sons in his only Son, is a reality infinitely higher than what he causes us to be by our nature, i.e. his creatures, the Name "Father" is, for us, an infinitely fuller version of the Name YHWH.
Moreover, Jesus revealed also that the reason for this infinitely better supernatural new creation is that God the Father loved us even as He loved his Son (Jn 17:23), which was clearly demonstrated by the infinite cost that God willed to bear to carry out that new creation, namely the passion and death of his Son in his assumed human nature. Thus there are two reasons why Father is, for us, an infinitely fuller version of the divine Name: the infinitely better supernatural new creation that it refers to, and the infinitely greater love for us that said new creation shows, both by itself and by its cost.
References and notes
 Why did Jesus never address God by the name "Jehovah"?
 I usually capitalize the verb "to be" when it denotes Subsistent Being.
 When speaking of God the Father, the terms "First" and "Firstness" ("Primitas" in latin) are not meant in a temporal sense, since both the generation of the Son and the spiration of the Holy Spirit are eternal.
 The different scopes of meaning of Latin "causa" and Greek "aitia" are most evident in the bull "Laetentur Caeli" from the (Roman Catholic) Ecumenical Council of Florence, when it says: "thereby also the Son should be signified, according to the Greeks indeed as cause, and according to the Latins as principle of the subsistence of the Holy Spirit, just like the Father."
Note to Roman Catholics: The last part of this answer follows the Franciscan theological tradition in trinitarian theology, whose main line is Greek Fathers - Richard of Saint Victor - Alexander of Hales - St. Bonaventure, and which posits an emanation account of the distinction between the Persons and understands the Father's innascibility in a positive way as Firstness, thus holding a pre-relational notion of God the Father (i.e. it is because He is First that He begets and thus is Father). Those following the Dominican theological tradition in trinitarian theology, particularly Thomists, will disagree with that.