If there is one only God why are there three different words which mean God?

The answer to this question becomes theological as much as linguistic. The very short version:

As the historical-critical method developed in the era of modern Biblical interpretation, scholars identified the fact that there were different words for God (including Jehovah and Elohim). These scholars become convinced that these different names reflected different/competing textual traditions (often referred to as "J" and "E") that were eventually merged together (textually) at a later period of time. ¹ Most of these scholars subscribe to the idea that different Biblical texts should be read and interpreted individually and that they cannot necessarily be reconciled with the point of view of another. ²

For those inclined to view the Bible as being internally (and doctrinally) consistent, the use of different names for God in the Old Testament would be attributed with God's attempt to reveal different aspects of His divine character through the different names and titles by which He has revealed Himself to mankind. ³

^{(1) Michael D. Coogan, "Introduction," in The Oxford Handbook of Biblical Studies, ed. J.W. Rogerson and Judith M. Lieu (Oxford: Oxford University Press, 2006), 6.}

^{(2) Ehrman, Bart D. An Introduction to the New Testament. 7th ed. (Grand Rapids, MI: William B. Eerdmans Publishing Company, 2019), 15.}

^{(3) Blue Letter Bible's The Names of God in the Old Testament}

Name forms

In ancient languages, as in modern vernacular, there can be, and are, different forms and spellings for the same noun (or name). For example, take the modern name, Elizabeth. On occasion this "one person" is referred to as Eliza, Lizzy, Betty, Lisa, as well as Elizabeth!

For the writers of the Bible, or the actors in the stories of the Bible, to use El, Elohim, etc. would not be a problem. (Some linguists see a plurality within some of the variants. Consider Genesis 1 where God uses "us" to reveal His compound nature.)

Note that "El" was of common use among the people where the Ebla Tablets were found, before the Bible was written. (Eastern Mediterranean region. In the Bible it is generic, with YHWH being the proper, revealed Name of God. [See any book on Mideast Archaeology, or Bible Dictionary, for in depth research.]

It was common in very ancient times for people groups to borrow words from each other, without accepting the detailed or specific connotations or definitions of them. Recall that the number of words in nations was much more limited than today, where there are dictionaries of thousands of pages containing millions of words (i.e. Merriam/Websters Dictionary of the English Language). Especially among people groups that had commerce and trade with each other, there would be a need to borrow words in order to communicate generally.

A modern example is found in the translation of the Greek Bible into Arabic dialects. The word for God in Arabic is Allah. And it is used to translate the generic word for God., It is not brought over into the translations with the idea or thought behind it that assumes this word is referring to the 600 A.D. connotations that Muslims apply to it. It is just used as a generic word.

In like manner, the ancient Arameans would use El, Elohim, etc for God but with different meanings among the different people groups. The Hebrews were not accepting pagan polytheism when using this word. Worship of God was monotheistic, whether the literary form was a singular or compound plural usage. (Compare, for example, the use of "One" in Deuteronomy 6:4, where "one" is used of a "cluster" of grapes.)

Much later in Jewish (and human history), the proper name, YHWH (Jehovah) was revealed through Moses, identifying the generic god.

New Testament Example
While Christ was on the cross He yelled out, My God, My God, why hast thou forsaken Me? (Matthew 27:46; Similar to Psalm 22:1) Notice that the word for "My God!" was eli, which was a mixture of the Aramaic and Hebrew. (Thayer's Lexicon of Greek Words, p. 277) Recall that El by itself is merely "God". But with the additional syllable, it became "My God!"

Does the two different words imply two different Gods? No, because "combining" words is common in linguistics.

And notice that when Mark relates the same story, he used the Eloi form (a Syriac form for the Hebrew, p. 206; Mark 15:34) Which being interpreted into Greek, was o theos mou, and into English, "My God!" So here is another form in use in linguistics, but not with any implication of "another Being." All the forms refer to Father God, whom Jesus was adddressing.

If there is one only God why are there three different words which mean God?

Consider a different question:

If there is only one American flag why are there three different names that refer to it? [The Star-Spangled Banner, Old Glory, The Stars and Stripes]

The first question has no more significance than the second (i.e. none at all).

Or compare with Colossians 2:6:

As ye have therefore received Christ Jesus the Lord, so walk ye in him

The same person is referred to by three different names, but is the one Jesus.

אלהים refers to God's two hands or two angels. One that blesses and one that curses.

אל שדי or the angel of blessing refers to the Angel that blesses.

Exodus 6.3 and I appeared unto Abraham, unto Isaac, and unto Jacob, as God Almighty, but by My name YHWH I made Me not known to them.

אל עליון also refers to the angel that blesses.

Genesis 14.19 And he blessed him, and said: 'Blessed be Abram of God Most High, Maker of heaven and earth;

יהוה refers to God's back

Exodus 33.23 And I will take away My hand, and thou shalt see My back; but My face shall not be seen.'

The angel or cursing appeared to Bilaam.

Numbers 22.22 And God's anger was kindled because he went; and the angel of the LORD placed himself in the way for an adversary against him.--Now he was riding upon his ass, and his two servants were with him

.

This angel also went down to Sodom. Also went down to Egypt to curse them with plagues. And also destroyed Canaan.

Joshua 5.15 And the captain of the LORD'S host said unto Joshua: 'Put off thy shoe from off thy foot; for the place whereon thou standest is holy.' And Joshua did so.

Why did he bow to the angel of destruction? He recognized it was the hand of God that executes justice against the evil. Whereas the other hand or angel executes blessings to the righteous.

Exodus 13.16 And it shall be for a sign upon thy hand, and for frontlets between thine eyes; for with a mighty hand the LORD brought us forth out of Egypt

The angel or cursing who curses Egypt.

Genesis 32.30 And Jacob asked him, and said: 'Tell me, I pray thee, thy name.' And he said: 'Wherefore is it that thou dost ask after my name?' And he blessed him there.

Here Jacob meets the angel who blesses.

The ark or the covenant very clearly conveys two hands and God above. This is the three.

As with a man his hands are part of him not seperate beings. So too with the hands of God. Three parts to one being.