Many theophoric names incorporate the theophoric element יָהּ, which is part of the Tetragrammaton.1 This theophoric element occurs alone approximately 49 times in 45 verses in the Old Testament.
For example, in Psa. 115:18, it is written,

Because it occurs in isolation as יָהּ, pronounced /yah/, we know the partial pronunciation of the Tetragrammaton יהוה.
The following image shows four theophoric names, all composed of the theophoric element יָהּ either preceded or followed by the same verb חנן (“he is gracious”). Thus, all the names share the same meaning: “Yah is gracious.” The image demonstrates how the vowel pointing in the theophoric name יָהּ changes depending on its position in the word (relative to the verb).

Theophoric element occurs in the beginning of the theophoric name
The theophoric element sometimes occurs at the beginning of a name. For example, the name יְהוֹחָנָן (Yehochanan)2 begins with the syllables /ye-ho/ represented by the Hebrew יְהוֹ. A contracted variant also occurs as יוֹחָנָן (Yochanan),3 beginning with the syllable /yo/ represented by the Hebrew יוֹ.
Theophoric element occurs at the end of the theophoric name
Other times, the theophoric element occurs at the end of a name. For example, the name חֲנַנְיָהוּ (Chananyahu)4 ends with the syllables /ya-hu/ represented by the Hebrew יָּהוּ. It also occurs as חֲנַנְיָה (Chananyah),5 ending with the syllable /yah/ represented by the Hebrew יָּה.
While all these names are recognized as theophoric, the different sounds of the theophoric element in each (i.e., /yah/ v. /yeh/) cause confusion for some concerning the pronunciation of the Tetragrammaton.
The Pronounciation “Jehovah” /dʒəˈhoʊvə/ or “Yehovah” /jəˈhoʊvə/
Concerning this pronunciation, Hans H. Spoer wrote,6
The pronunciation of the tetragrammaton as “Jehovah” is an absurdity. The earliest appearance of this transliteration we find in two passages of the “Pugio Fidei,” 1278, though it is not improbable that this is due to a later copyist. We know for certain, however, that this misnomer was brought into prominence by Petrus Galatinus, confessor of Leo X. The discontinuation of the pronunciation of the tetragrammaton by the Jews is doubtless due to a misinterpretation of Lev. 24:11, 16, in consequence of which the name was considered too sacred to be pronounced.
The pronunciation “Jehovah/Yehovah” was caused by the Masoretes inserting the vowel pointing for אֲדֹנָי (“Lord”) under the Tetragrammaton יהוה.
Marvin R. Wilson wrote,7
The name Jehovah is a hybrid proper name that combines the consonants of YHWH with the vowels of Adonai. The Masoretes, Jewish scholars from the early Middle Ages who established the basic text for the Hebrew Bible and standardized its pronunciation, inserted the vowels of Adonai into the Tetragrammaton. They did this to remind readers to avoid saying the sacred name Yahweh and to substitute instead the name Adonai. In the late Middle Ages, and especially at the time of the Reformation, a Christian misunderstanding of the (vocalized) Masoretic text resulted in the expression Jehovah finding its way into common Christian usage.

This tradition of reciting אֲדֹנָי for יהוה predates the Masoretes by centuries. This explains why the Jewish scribes who produced the Septugaint wrote the word κύριος (equivalent to אֲדֹנָי) for occurrences of יהוה, rather than simply transliterating the Tetragrammaton into Greek.
The Pronunciation “Yahweh” /ˈjɑːˌweɪ/
Some contend that “Yahweh” /ˈjɑːˌweɪ/ cannot be the true pronunciation of the Tetragrammaton since the Tetragrammaton contains the Hebrew letter ו, which they suppose must be pronounced like the English letter “v”—as a voiced labio-dental fricative (IPA /v/). While the Hebrew letter ו is pronounced as a voiced labio-dental fricative in modern Hebrew, most linguistics agree that it was pronounced as a voiced labio-velar approximant (IPA /w/) in biblical Hebrew (like the Arabic و and Syriac ܘ).
HALOT states,8

For example, instead of a name such as דָּוִד (“David”) being pronounced /daˈvid/, it would have been pronounced /daːˈwiːð/. If we were to transliterate these into English, the former (modern Hebrew) would be “David,” while the latter (biblical Hebrew) would be “Dawid.” That being said, it is the accepted standard to transliterate the Hebrew letter ו into English by the letter “v” regardless of it being used in a biblical or modern Hebrew context. It is left up to the reader to pronounce it as /v/ or /w/ depending on the context.
Thus, “Yahweh” may also be written as “Yahveh” with the understanding that the letter “v” in the latter should be pronounced as /w/ rather than /v/ to reflect the biblical Hebrew pronunciation.
Propretonic reduction
To account for the change in pronunciation of the theophoric element from /yah(u)/ to /yeh(o)/ is the grammatical phenomenon known as “propretonic reduction,” or simply, vowel reduction.
Propretonic reduction causes the change from /yah/ to /yeh/ when the theophoric element is located at the beginning of the theophoric name since the tonic syllable shifts from the beginning to the end of the name.

On the other hand, it does not cause the change from /yah/ to /yeh/ when the theophoric element is located at the end of the theophoric name since the theophoric element remains the tonic syllable.9
(more to come...)
References
Koehler, Ludwig; Baumgartner, Walter. A Hebrew and Aramaic Lexicon of the Old Testament. Trans. Richardson, M. E. J. Ed. Baumgartner, Walter; Stamm, Johann Jakob. Leiden: Brill, 2002.
Spoer, Hans H. The Origin and Interpretation of the Tetragrammaton. Chicago: U of Chicago P, 1899.
The Jewish Encyclopedia. Ed. Singer, Isidore. Vol. 12. New York: Funk, 1907.
Wilson, Marvin R. Exploring Our Hebraic Heritage: A Christian Theology of Roots and Renewal. Grand Rapids: Eerdmans, 2014.
Footnotes
1 The Jewish Encyclopedia. Vol. 12, p. 120, “Tetragrammaton”
2 Ezra 10:6; often found transliterated in English versions of the Bible as “Jehohanan”
3 Neh. 12:23; often found transliterated in English versions of the Bible as “Johanan”
4 1 Kings 17:1; found transliterated in English versions of the Bible as “Hahaniah”
5 2 Kings 1:4; also found transliterated in English versions of the Bible as “Hananiah”
6 p. 27
7 p. 138
8 p. 257
9 The majority of Hebrew words are stressed on the final syllable, unlike English where many words are stressed on the initial syllable. For example, while English speakers pronounce the name דָּוִד as /daˈvid/—stressing the initial syllable, modern Hebrew speakers pronounce it as /davidˈ/—stressing the final syllable.