In Matthew 27:45-46 Jesus is recorded as saying:
Eli, Eli, lema sabachthani?
Based on Jesus the Phoenician Jesus called God 'EL'—which is a Phoenician God—when he was on the cross. Is this claim true or false? Did Jesus call God YHWH?
No. The tetragrammaton was not used in Jesus' time. Faithful Jews would avoid saying it so as to not transgress the third commandment. The most common circumlocution was "Lord" (Andonai in Hebrew or Kurios in Greek), though he might also be referred to simply as "Heaven."
In answer to Jesus using El from the cross. El is the common word for God from all over the ancient near east. It appears in Biblical Hebrew to refer to the God worshiped by Jews in Psalm 18:2[H3]1, 30[H31], 32[H33], 47[H48]; 22:1[H2], 10[H11]; 68:20[H21]; Job 8:3, 4, and 13; and others. This name (El instead of Eloh or Elohim) is more common in poetry than in prose. It can also be used to refer to idols (as in Exodus 34:14; Isaiah 44:10, 15; Psalm 81:9[H10]; and others), but it is also a name for the Hebrew God as seen when Jesus quoted Psalm 22 from the cross:
Psalm 22:1 My God, my God, why have you abandoned me?...
The Greek letters in Matthew 27:45 (ἠλι ἠλι λεμα) are a perfectly good transliteration of the first three Hebrew words in Psalm 22:1[H22], אלי אלי למה. Regarding the word for "abandoned", instead of the Biblical Hebrew 'azab (עזבתני) from the Psalm, Matthew transliterates the Mishnaic Hebrew word sabak with σαβαχθανι. The root sabak is found in both Aramaic and Mishnaic Hebrew.2
You will note that is the cry from the cross. The first two words are אלי אלי which is the Hebrew spelling of Eli, Eli. The long i ending is the first person possessive in Hebrew. אלי אלי means "My God, my God."
In the Hebrew Bible, it can be seen that El, YHWH, and Eloh(im) all refer to the same deity. For example,
18:30 [El] acts in a faithful manner; [YHWH]’s promise is reliable; he is a shield to all who take shelter in him. 18:31 Indeed, who is [Eloh] besides the [YHWH]? Who is a protector besides our [Eloh]?
You can see that El and YHWH act the same (reliably and faithfully). The next verse states outright that Eloh is the same as YHWH. Thus, YHWH, El, and Eloh are the same being in this Psalm. There are clearly places where El is not YHWH (see above for the idolatry references). However, in Psalm 22, it is clearly a reference to YHWH.
And thus, Jesus used El because that was an accepted name for YHWH, especially when quoting a poem that used it.
1In the Psalms, the Hebrew verse references are often 1 off of the English because the Hebrews count the heading as the first verse.
2David Bivin and Roy Blizzard Jr., Understanding the Difficult Words of Jesus, 10.
Jesus spoke primarily Aramaic followed by Hebrew and Greek. Since most of the new testament was written in greek, you will probably never find it recorded that Jesus said "YHWH" in scriptures. This doesn't mean he didn't say it, it's just a translation thing.
Furthermore, it was Hebrew tradition to interpose the name Adonai inside of "YHWH" which is translated in the old testament as LORD. Out of reverence for God, it was tradition never to speak the name of God, so when Hebrews read this word, they would say "Adonai" - lord. This was because it was believed that to know a god's true, secret name was to be able to control this god. There was power in a name (hence Moses' question at the burning bush - "Who should I say has sent me" and God's shrewd response). Therefore, we can assume Jesus probably did this, but we have no way to know for sure because if he spoke it in Hebrew, it was recorded in Greek.
One of the oldest recorded gods is El, the mountain god. When the Hebrew language evolved, it is thought that the word translated as "lord" or "lords" (lower case) - Elohim derives from the name of the oldest recorded god, El. El was a Sumerian and Akkadian god long before he was Phoenecian. Any reference to El, should probably be read as a reference to Yahweh. http://en.wikipedia.org/wiki/El_(deity)